TABLE  OF  CUBIC  YARDS  IN  LENGTHS  OF  100  FEET. 

ADAPTED  ESPECIALLY  TO  THE  CALCULATION  OF  EAETH  WOKK  BY  THE  METHOD  OF  ATEKAGING  E>'D  AREAS. 


Contents  of  Column  "A"  are  for  the  integers  in  column  headed  "Area,  Square  Feet." 
Contents  of  Column  "B"  are  for  the  same  integers  plus  0.5  square  foot. 


Contents  for  lengths  greater  or  less  than  100  are  obtained  by  simple  proportion,  thus  :  125 
sq.  ft.  for  length  of  20  &.=j%%=\  of  463.0  cu.  yds.;  the  contents  for  125  sq.  ft.=92.6  cu.  yds. 


COPYRIGHT  1885  BY  S.  B.  FISHER. 


Contppts, 

Coutents, 

Contents, 

Coiitfiiis, 

Contents, 

Ch.  Yds. 

I II. 

1  Us. 

Cn.  Yd^. 

*■  ^ 

Cn.  Yds. 

«3  £ 

i. 

Cn.  Yds. 

A. 

B. 

^  qO 

A. 

B. 

(Ml 

A. 

B. 

A. 

B. 

A. 

B. 

1.8 

100 

370.4 

372.2 

200 

740.7 

742.6 

300 

1111,1 

1113.0 

400 

1481.5 

1483  3 

1 

3.7 

5.6 

1 

374.1 

375.9 

1 

744.4 

746.3 

1 

1114.8 

1 116  7 

1 

1485.2 

1487.0 

2 

7  4. 

2 

377.8 

379.6 

2 

748.1 

750  0 

2 

1118.5 

1120.4 

2 

1488.9 

1490.7 

3 

11.1 

13.0 

3 

381.5 

383.3 

3 

751.9 

753.7 

3 

1122.2 

1124.1 

3 

1492.6 

1494  4 

4 

14.8 

16.7 

4 

385.2 

387.0 

4 

755.6 

757.4 

4 

1 125.  li 

1 127  8 

4 

1496.3 

1498.1 

5 

18.5 

5 

388.9 

.390.7 

5 

759.3 

761.1 

6 

1129.(; 

1131.5 

6 

1500.0 

1501.8 

6 

22.2 

24.1 

6 

392.6 

394,4 

6 

763  0 

761.8 

6 

1133.3 

1 135.2 

6 

1503  7 

1505.0 

7 

2.S.C 

27.8 

7 

396  3 

39S.1 

7 

766  7 

768.5 

7 

1137.1 

1138.9 

7 

1507.4 

1509.3 

8 

29.6 

31.5 

8 

400  0 

401.8 

8 

770.4 

772  2 

8 

1140.7 

1142.  1 

8 

1511  1 

1513.0 

9 

33.5 

35.2 

9 

403.7 

405.6 

9 

774.1 

775.9 

9 

1144.4 

1146.3 

9 

1514.8 

1516.7 

10 

37. C 

38.9 

110 

407.4 

409.3 

2K' 

777.8 

779.6 

310 

1148  1 

1 150.11 

41<i 

1518.5 

1 520.4 

1 

40  7 

42.6 

1 

411.1 

413.0 

] 

781.5 

783.3 

1 

1 151.9 

1 153  7 

1 

1522  2 

1.524.1 

2 

44A 

46.3 

2 

414.8 

416.7 

2 

785.2 

787.0 

2 

1155  6 

1157.4 

2 

1525  9 

1527.8 

3 

48.1 

50.0 

3 

418  5 

420.4 

3 

788.9 

790.7 

3 

1159  3 

1161.1 

3 

1529  6 

1531.5 

i 

51.9 

53.7 

4 

422  2 

424.1 

4 

792.6 

794.4 

4 

U63.0 

1164.8 

4 

1533.3 

1535.2 

5 

65.6 

57.4 

5 

425.9 

427.8 

5 

796.3 

798.1 

5 

1166.7 

1168.5 

5 

1537.0 

1538.9 

6 

59.S 

61.1 

6 

4296 

431.5 

6 

8or.o 

801.8 

G 

1170.4 

1172.2 

*  6 

1540.7 

1542.6 

7 

63.  C 

61  8 

7 

433  3 

435.2 

7 

803.7 

805.6 

7 

1 174.1 

1175  9 

7 

1544.4 

1546.3 

8 

66.7 

68.5 

8 

437.0 

438  9 

8 

807.4 

809.3 

8 

1177.8 

1179.6 

8 

1548.1 

1550.0 

» 

70.4 

72  2 

9 

440  7 

442.6 

9 

811.1 

813.0 

9 

118L5 

11833 

9 

1551.9 

1553.7 

20 

74.1 

75.9 

120 

414.4 

416.3 

220 

814.8 

816.7 

320 

1185.2 

1187.0 

42o 

1555.6 

1667.4 

1 

77.8 

79.6 

1 

448  1 

4.50.0 

1 

818.5 

820.4 

1 

1188  9 

1190.7 

1 

1559.3 

1561.1 

2 

81.5 

83.3 

2 

451.9 

453.7 

2 

822.2 

824,1 

2 

1192.6 

11944 

2 

1563.0 

1564.8 

3 

85.2 

87.0 

3 

455.6 

457.4 

3 

825.9 

827.8 

3 

1196.3 

1198.1 

8 

1566.7 

1568.5 

4 

88.9 

90.7 

4 

459  3 

461.1 

4 

829.6 

831.5 

4 

1200  0 

1201.8 

4 

1570.4 

1572.2 

5 

92  6 

91.4 

6 

463.0 

404.8 

833.3 

835.2 

5 

1203.7 

1205.6 

5 

1574.1 

1576.9 

6 

96.3 

98.1 

G 

400  7 

408.5 

6 

837.0 

838.9 

6 

1207.4 

1209.3 

6 

1577.8 

1679.6 

7 

loo  0 

101,8 

7 

470.4 

472.2 

7 

840.7 

842.6 

7 

1211.1 

1213.0 

7 

1581.5 

1583.3 

8 

103.7 

105.0 

8 

474.1 

475.9 

8 

844.4 

846  3 

8 

1214.8 

1216.7 

8 

1685.2 

1687.0 

9 

107.4 

109.3 

9 

477.8 

479.0 
483.3 

9 

230 

848.1 

850.0 

9 

1218  6 

1220.4 

9 

1588.9 

1690.7 

30 

•lll.l 

113.0 

130 

481.5 

851.9 

853.7 

331* 

1222.2 

1224.1 

430 

1592.6 

1594.4 

1 

114.8 

110.7 

1 

485.2 

487.0 

1 

855.6 

857.4 

1 

1225.9 

1227.8 

1 

1590.3 

1598.1 

2 

118.5 

120.4 

2 

488.9 

490.7 

2 

859.3 

861.1 

2 

1229.6 

1231.5 

2 

1600.0 

1601.8 

3 

122.2 

124.1 

3 

492.6 

491.4 

3 

863.0 

864.8 

3 

1233.3 

1235.2 

3 

1603.7 

1605.6 

4 

125.9 

127.8 

4 

490.3 

493.1 

4 

806.7 

863  5 

4 

1237.0 

1238.9 

4 

1607.4 

1609.3 

5 

129.6 

131.5 

5 

500.0 

501.8 

5 

870  4 

872  2 

5 

1240.7 

1242.0 

5 

1611.1 

1613.0 

C 

l.^l  3 

135.2 

6 

503.7 

505.0 

6 

874.1 

875,9 

6 

1244.4 

1210.3 

6 

1614.8 

1616.7 

7 

137.0 

133,9 

7 

507.4 

509.3 

7 

877.8 

879.6 

7 

1248  1 

1250  0 

« 

1618.5 

1620.4 

8 

140.7 

142.6 

8 

511.1 

513.0 

8 

881.5 

883.3 

8 

1251.9 

1253.7 

8 

1622.2 

1624.1 

9 

144.4 

143.3 

9 

514.8 

516.7 

9 

885.2 

887.0 

9 

1255.6 

1257.4 

9 

1625.9 

1627.8 

40 

148  1 

150.0 

14o 

518.5 

520.4 

240 

883  9 

890.7 

340 

1259.3 

1261.1 

440 

1629  6 

1631.5 

1 

151.9 

153.7 

1 

522.2 

521.1 

1 

892.6 

89 1.4 

I 

1263.0 

1264  8 

1 

1633.3 

1635.2 

2 

1 55.6 

157.4 

2 

525.9 

527.-8 

2 

890.3 

893.1 

2 

1266.7 

1 268.-" 

,  2 

1637.0 

1638.9 

3 

150.3 

101.1 

3 

529.6 

531.5 

3 

900  0 

901.8 

3 

1270.4 

1272.- 

3 

1640.7 

1642.0 

4 

1G3.0 

101.8 

4 

533.3 

535.2 

4 

903.7 

9U5.0 

4 

1274.1 

1275.9 

4 

1644.4 

1046.3 

5 

103.7 

103.5 

5 

537  0 

533.9 

5 

907.4 

909.3 

5 

1277.8 

12790 

5 

1648.1 

1650.0 

6 

170.4 

172.2 

6 

540.7 

542.6 

6 

911.1 

913.0 

6 

1231.5 

12i3.3 

6 

1651.9 

1653.7 

7 

174.1 

175.9 

7 

544.4 

546.3 

7 

914.8 

916,7 

7 

1285.2 

1287.0 

7 

1655.6 

1657.4 

8 

177.8 

179.0 

8 

543.1 

550.0 

8 

918.5 

920.4 

8 

1283.9 

1290.7 

8 

1659.3 

1661.1 

9 

181.5 

18.3  3 

9 

551.9 

553.7 

9 

922.2 

924  1 

9 

1.92.6 

1291.4 

9 

1663.0 

1664.8 

50 

135.2 

187.0 

150 

555.0 

557.4 

250 

925.9 

927.8 

350 

1296.3 

1298.1 

450 

1666.7 

1668.5 

1 

13S.9 

190.7 

1 

559  3 

531.1 

1 

929.6 

931.5 

1 

1300.0 

1301.8 

1 

1670.4 

1672.2 

2 

102  6 

191.4 

2 

503.0 

504.8 

2 

933.3 

9352 

2 

1303.7 

1305.0 

2 

1674.1 

1675.9 

8 

193.3 

193.1 

3 

506  7 

668  5 

3 

937.0 

9319 

3 

1307.4 

1309.3 

3 

1677.8 

1679.6 

4 

200.0 

201.8 

4 

570.4 

572  2 

4 

940.7 

942.6 

4 

1311.1 

1313.0 

4 

1681.5 

1683.3 

203.7 

205.0 

5 

574.1 

675.9 

5 

914.1 

946.3 

5 

1314.8 

1316.7 

5 

1685.2 

1687.0 

G 

207.4 

209.3 

6 

•577.8 

679.0 

6 

918.1 

950.0 

6 

1318.5 

1320.4 

6 

1688.9 

1690.7 

7 

211.1 

213.0 

7 

581.5 

583.3 

7 

951.9 

953.7 

7 

1322  2 

1324.1 

7 

1692.6 

1694,4 

8 

214.8 

210.7 

8 

585.2 

.587.0 

8 

955  6 

957,4 

8 

1325.9 

1.327.8 

8 

1696.3 

1698.1 

9 

218.5 

220.4 

9 

588.9 

590.7 

9 

959.3 

961.1 

9 

1329.6 

1331  5 

9 

1700.0 

1701.8 

60 

222  2 

224.1 

160 

592  6 

694  4 

260 

963.0 

964,8 

860 

1333,3 

1335.2 

4Go 

1703.7 

1706.6 

1 

225,9 

227.8 

] 

5963 

598.1 

1 

906.7 

968.5 

1 

1337.0 

1338.9 

1 

1707.4 

1709.3 

2 

229.6 

231.5 

2 

600.0 

6018 

2 

9704 

972.2 

2 

134o!7 

1342.6 

2 

1711.1 

1713.0 

3 

233.3 

235.2 

8 

003  7 

605  6 

3 

974.1 

975.9 

3 

1344.4 

1346  3 

3 

1714.8 

1716.7 

4 

237.0 

238.9 

4 

607.4 

009.3 

4 

977.8 

979.6 

4 

1348.1 

1350.0 

4 

1718.5 

1720.4 

5 

210  7 

242.0 

5 

611.1 

613.0 

5 

931.5 

983.3 

5 

1351.9 

1353.7 

5 

1722.2 

1724.1 

6 

244.4 

246.3 

6 

014.8 

616.7 

6 

985.2 

987.0 

6 

1355.6 

1357.4 

6 

1725.9 

1727.8 

7 

248.1 

250.0 

7 

018.5 

620.4 

7 

988  9 

990.7 

7 

1359.3 

1361  1 

7 

1729.6 

1731.5 

8 

251.9 

253.7 

8 

022.2 

024.1 

8 

992.6 

994.4 

8 

1363.0 

1364.8 

8 

1733.3 

1735-2 

9 

2")5.6 

257.4 

9 

025  9 

627.8 

9 

996.3 

998  1 

9 

1366.7 

1368.5 

9 

1737.0 

1738.9 

70 

259  3 

261.1 

17i« 

029.6 

631.5 

27'HOOO.O  1001.8 

370 

1370.4 

1372.2 

470 

1740.7 

1742.6 

1 

2  :;3,o 

264.8 

1 

033.3 

635.2 

1  1003.7  1005.6 

1 

1374.1 

1375.9 

1 

1744.4 

1746.3 

2 

200  7 

268.5 

i; 

637.0 

638.9 

2  1007  4  1009.3 

2 

1377.8 

1379.6 

2 

1748.1 

1760.0 

3 

270.4 

272.2 

3 

640  7 

642.6 

3  101 1.1  1013.0 

3 

1381.6 

1383.3 

3 

1751.9 

1753.7 

4 

274.1 

275.9 

4 

644  4 

646.3 

4  1014.8  1016.7 

4 

1385.2 

1387.0 

4 

1755.6 

1757.4 

5 

277.8 

279.6 

5 

648.1 

650.0 

5  1018.5  1020.4 

•' 

1388^9 

1390.7 

5 

1759,3 

1761.1 

6 

281.5 

283.3 

6 

051.9 

653.7 

6  1022.2  1024.1 

6 

1392.6 

1394.4 

6 

1763,0 

1764.8 

7 

285.2 

287.0 

7 

655  6 

657.4 

7  1025.9  1027.8 

7 

1396.3 

1398  1 

7 

1766.7 

1768.5 

8 

288.9 

290^7 

8 

0i9.3 

661  1 

8  1029.6  1031.5 

8 

1400.0 

1401.8 

8 

1770.4 

1772  2 

9 

292  6 

294.4 

9 

663  0 

604.8 

9  1033.3  1035.2 

0 

1403.7 

1405.6 

9 

1774.1 

1775.9 

80 

2903 

298,1 

180 

666.7 

668.5 

280  1037.0  1038.9 

380 

1407.4 

1409.3 

480 

1777.8 

1779.6 

1 

300.0 

301.8 

1 

670.4 

672.2' 

1  1040.7  1042.6 

1 

1.411.1 

1413.0 

1 

1781.5 

1783.3 

2 

3o3.7 

305!6 

2 

674  1 

675.9 

2  1044.4  1046  3 

2 

1414.8 

1416.7 

2 

1785.2 

1787^0 

3 

307.4 

309.3 

3 

677.8 

679.6 

3  1048.1  1050.0 

3 

1418.5 

1420  4 

3 

1788.9 

1790.7 

4 

311.1 

313.0 

4 

681  5 

683.3 

4  1051.9  1053.7 

4 

1422.2 

1424.1 

4ll792,6 

1794.4 

t 
«» 

314.8 

316.7 

c 
O 

685.2 

687.0 

6  1055.6  1057.4 

t 
o 

1425.9 

1427.8 

6  1796.3 

1798.1 

6 

318.5 

320.4 

6 

688.9 

690.7 

6  1059  3  1061.1 

6 

1429.6 

1431.5 

6 

1800.0 

1801.8 

7 

322.2 

3241 

7 

092.6 

694.4 

7  1063.0  1064.8 

7 

1433.3 

1435.2 

7 

1803.7 

1806,6 

8 

325.9 

327.8 

8 

696.3 

698.1 

8  1066.7  1068.5 

8 

1437.0 

1438.9 

8 

1807.4 

1809.3 

9 

329,6 

331.5 

9 

700.0 

701.8 

9  1070.4  1072.2 

9 

1440.7 

1442.6 

9 

1811.1 

1813.0 

.  90 

333.3 

335.2 

190 

703.7 

705.6 

29(1  1074.1 

1075.9 

390 

1444.4 

1446.3 

490 

18148 

1816.7 

1 

337.0 

338.9 

1 

707.4 

709.3 

1,1077.8 

1079.6 

1 

1448.1 

1450.0 

1 

1818.5 

1820.4 

2 

310.7 

342.6 

2 

711.1 

713.0 

2  1081-5 

1083.3 

2 

1451.9 

1453.7 

2 

1822.2 

1824.1 

3 

344.4 

346.3 

3 

714.8 

716.7 

3 

10S5.2 

1087.0 

3 

1455  6  1457.4 

3 

1825.9 

1827.8 

4 

3181 

350.0 

4 

718.5 

-^20.4 

4 

1088.9 

1090.7 

4 

1459.3  1461.1 

4  1829.6 

1831.5 

5 

351.9 

353.7 

5 

722.2 

724.1 

5 

1092.6 

1094.4 

5 

1463.0  1464,8 

5  1833.3 

1835.2 

C 

3-)5.6 

357,4 

6 

725.9 

727.8 

6 

1096.3 

1098.1 

6 

1466.7  1468.5 

6  1837.0 

1838.9 

7 

359.3 

361.1 

7 

729  6 

731.5 

7 

1100.0 

1101.8 

7 

1470.4  1472.2 

7  1840.7 

1842,6 

8 

363.0 

364.8 

8 

733  3 

735.2 

8 

1103.7 

1105.6 

8 

1474,1  1475.9 

8' 

1844.4 

1846.3 

9 

366.7 

368.5 

9 

737.0 

738.9 

9 

1107.4 

1109.3 

9 

1477.8  1479.6 

9  1848.1 

1850.0 

100 

370.4 

372.2 

200 

740.7 

742.6 

300 

1111.1 

1113.0 

400 

1481.5  1483.3 

500.1851.9 

1853.7 

500  1851.9 

1  1855.6 

2  1859.3 

3  1863.0 

4  1866  7 


8 
9 

510 
1 
2 
3 
4 
6 
6 
7 
8 
9 

520 
1 
2 


4 

5 
G 
7 
8 
9 

530 
1 
2 
3 
4 

G 
7 

8 
9 

540 
1 


Content.s, 
Cu.  Yd>i. 


185.3.7 
1857.4 
1861.1 
1864.8 
1 868.5 

5  1870.4  1872.2 

6  1874.1 
1877.8 
1881.5 
1885.2 
1888.9 
1892.6 
1896.3 
1900.0 
1903.7 
1907.4 
1911.1 
1914.8 
1918.5 
1922.2 
1925,9 
1929.6 
1933.3 

3  1937.0 
1940.7 
1944.4 
1948.1 
1951.9 
1955.6 
1959.3 
1963.0 
1966.7 
1970.4 
1974.1 
1977.8 
1981.5 


B. 


1875.9 
1879.6 
1883.3 
1887.0 
1890  7 
1894.4 
1898.1 
1901.8 
1905.6 
1909.3 
1913.0 
1916.7 
1920.1 
1924.1 
1927.8 
1931.5 
1935.2 
1938.9 
1942.6 
1946.3 
1950.0 
1953.7 
1957.4 
1961.1 
1904.8 
1968.5 
1972.2 
1975.9 
1979.6 
1983  3 


1985.2  1987.0 


1988.9 
199 
1996.3 


2000.0  2001.8 


2003.7 


2  2007.4  2009  ■■ 


2011.1 


2014.8  2010.7 


5  2018.6 
"6  2022.2 

7  2025.9 

8  2029.6 


2020.4 
2024.1 
2027.8 
2031.5 


2033.3  2035.2 
550  2037.0  2038,9 


1  2040.7 


2  2041.4  2046.3 


2050.0 

2053. 

■2057.4 


3  2048.1 

4  2051.9 
b  20.55.6 

6  2059.3  2061  1 

7  2003.0  2064  8 

5  2000.7  2068.5 
9  2070.4  2072.2 


56  0  2074.1 


1990.7 
1994.1 
1998.1 


2005.0 


2013.0 


2042.6 


2075.9 


570 
1 

2 
3 


1  2077.8  2079.6 

2  2081  5  2083.3 

3  2085.2  2087.0 

4  2088  9  2090.7 
6  2092.6  2094.4 

6  2090.3  2098.1 

7  2100.0  2101.8 

8  2103.7  210.5.0 

9  2107.4 
2111.1 


2118.5 
2122-2 
4  2125.9 


6  2133.3 


7  2137.0  2138.9 


8  2140.7 


9 


580  2148.1 


590 
] 


600 


2109.3 
2113.0 
2114.8  2110.7 


2120.4 
2124.1 
2127.8 


2129.6  2131.5 


2144  4 


2135. 


2142.0 
2146.3 
21.50.0 


2151.9  2153.7 
2165.6  2157.4 
2159.3  2161.1 
2163.0  2161.3 


5  2106  7 
G  2170.4 

7  2174.1 

8  2177.8 

9  2181.5 


2168.5 
2172.2 
2175,9 
2179  0 
2183.3 
185.2  2187.0 
2190.7 


2188.9 

2  2192.6  2194.4 

3  2196.3  2198.1 

4  2200.0  2201.8 
6  2203.7  2205.6 

6  2207.4  2209.3 

7  2211  1  2213.0 

8  2214.8  2216.7 

9  2218.5  2220.4 
2222.2  2224.1 


Contents, 
Cn.  Yds. 


A. 


2224  1 
2227.8 
2-231.5 
2235.2 
2233.9 
2212.0 
2216.3 
2250.0 
2253  7 
22.57.4 
2261.1 
2264.S 
2268.5 
2272.2 
2275.9 
2279.0 
2283  3 


600  2222.2 
112225.9 
2j22-29.0 
32233.3 
412237.0 
512240.7 
62244.4 

7  2248.1 

8  2251.9 

9  2-255.6 
6  10,2259.3 

1' 2263  0 
2'2206.7 

3  2270.4 

4  2274.1 

5  2277.8 

6  2281.5 
7|2285  2|2287.0 

8  2288  9  2290.7 

9  2292.6  2294,4 
620  2-296.3  2298.1 

1  2300.0  2301.8 

2  2303.7  2305,6 

3  2307.4  2309.3 

4  2311.1  2313.0 

5  2314  8  2316,7 

6  2318  5'2320.4 

7  2322.2' 2324.1 

8  2325  9  2327.8 

9  2329.6 '233 1.5 
630  2333.3  23.35.2 

1  2337.0  233S.9 

2  2340.7:2312.6 

3  2344,4  2346.3 

4  2348.1  23-50.0 

5  2351.9  2353.7 

6  2355-6  2357.4 

7  2359.3  2301.1 

8  2303.0  2304.8 

9  2366.7  2368.5 
640  2370.4  2372.2 

1  2374.1  2375.9 

2  2377.8  2379.0 

3  2331.5  2383,3 
■^4  2385.2  2387.0 

5  2388.9  2390.7 

6  2392.6  2394.4 

7  2390.3  239-i.l 

8  2400.0  2401.8 

9  2403.7  2105.6 
650  2407.4  2409.3 

1  2411.1  2413.0 

2  2414.8  2416,7 

3  2418.5  2420.4 

4  2422  2  2424  1 
5'2425.9|2427  8 
6  2429.6,2431.5 
7j2433  3  2435.2 
8, 2437.0 '2438  9 
9  2440.7 1 24  42.0 

660 -2444  4  2440.3 
l'2448  1  2450.0 

2  2151,9  2453,7 

3  2456.6  2457.4 

4  2459.3  2461.1 
5 '2163.0  2464.8 

6  2466.7  2468  5 

7  2470.4  2472  2 
8'2474.1  2475.9 
9  2477.8  2479.ii 

670  2481.5124X3.3 

1  2485.2'2487.0 

2  2483.9 '2490.7 

3  2192.6'2494.4 

4  2  496.3:2498.1 

5  2500.0  2501.8 
2505.6 
2509.3 
2513.0 
2516.7 
2520.4 

l'2522.2j2524.1 

2  2525.9'2527.8 

3  2529.; '263 1.5 
412533.3  2535.2 

6  2537.0! 25.-i8.9 
6 
7 
8 


Comenls, 
Cu.  Yds. 


A. 


503.7 

7  2507.4 

8  2511.1 

9  2514.8 
680  2518.5 


2540  7  2542.0 
2544.4  2516.3 


2548  1  2560.0 
„  2551.9  2553.7 

69  0  25.55.6'2557.4 
25.59.3|2561.1 

2503.0  2504.8 

2566.7  2568.5 
2570,4,2572.2 

2574.1  2575.9 

2577.8  2579.6 
2581.5  2583.3 
2585.2:2587.0 

2588.9  2590.7 

70  0  2592.6  2594.4 


2 
3 
4 
5 
6 
7 
S 
9 

710 
1 

2 
3 


7 
8 
9 

720 
1 
2 
3 
4 


7 

8 
9 

730 


6 
7 

9 

r4o 
1 

2 


1 

2 

3 
4 
£ 
6 
7 
8 
9 

76(» 
1 


700  2-592.6  2594.4 
1  2-596.3,2598.1 
2600,0  2601.8 
2603.7  [2605.6 
•2607.4:2609.3 
2611.1,2613.0 
■2614.8  2616.7 

2618.5  2620,4 

8  2622,2  2624.1 
2625  9  2627.x 
2629  6  2'i31.5 
2633  3  2635 

2037.0  2638.9 
2640.7  2642.6 

4  2644,4  2646.3 

2648.1  2050.0 
G  2651.9  2653.7 

2655.6  2657.4 
2659.3  2661.1 

9  2663.0  2664.8 

2066.7  2068.-' 
2670.''j2H72.2 
2G74.1  267-").9 

2677.8  2679.6 
_  2681.5  2633.3 

5  2685.2  2087,0 

6  2088.9  2690.7 

2692.6  2694.4 
8  2696,3  2698.1 

2700.0-2701.8 

2703.7  2705.6 
1 '2707.4  2709.3 
212711.1  2713.0 
3I2714.8  2716.7 

4  2718.5  2720.4 

5  2722  2  2724.1 
2725-9  2727.8 
2729.0  2731.5 

2733.3  2735.2 
■2737.0  2738.9 

2740.7  2742.0 

2744.4  2746.3 
_  -2748.1  2750.0 

3  2751.9  2753.7 

4  2756.6  2767.4 
2759.3  2701.1 
■2703.0  2704.8 
27O6.7I2768.6 
2770.4'2772.2 
2774.l|2775.9 

75  0  2777.8'2779.6 
2781.52783.3 

2785.2  2787.0 
2788.912790.7 

792.6'2794.4 
.  2796.3  2798.1 

6  2800.0  2S01.8 
2803.7 12805.6 
2807.42809.3 
2811.12813.0 

2814.8  2816.7 

2318.5  2820.4 
_  2822.2  2824.1 
3  -2826.9  2827.8 
_  -2829  6  2831.5 

5  2833.3  -2835.2 

6  2837.0  2838  9 

7  2840  7  2842.6 

8  2844,4  2846.3 

9  2848.1  2850.0 
7  70' 285 1.9 -2853.7 

1  2855.6 '2857.4 

2  2869  3  2801.1 

3  2863.0  2864.8 

4  -2866.7  2868.5 

6  2870.4  2872  2 
G  2874.1  2876.9 

7  2877.8  2879.6 

8  -2881.5  2883.3 

9  2885.2  2887.0 
780  2888.9  2890.7 

1  2892.6  -2894.4 

2  2896.3  2898.1 

3  2900.0  2901.8 

4  2903.7  2905.0 
6  2907.4  2909  3 

6  2911.1  2913  0 

7  2914.8  2916.7 

8  2918.5  -2920.4 

9  2922.2  2924.1 
790  29-25.9  2927.8 

1  2929.6  2931.5 

2  2933.3  2935.2 

3  2937.0  2938  9 

4  2940.7  2942.6 
6  2944.4  2946.3 

6  2948.1  2950.0 

7  2951.9  2953.7 

8  2955.6  2957.4 

9  29.59.3  2961.1 
800  2963.0  2964.8 


1 

2 
3 
4 
i 
6 
7 
8 
9 

82(1 
1 
2 
3 
4 
5 
G 
7 
8 


86 


Contents, 
Cm.  Yds.  s^i, 


A. 


B. 


800  2963.0  2964,8 

1  2066.7  2968  5 

2  2970.4  2972.2 

3  -2974.1  2975,9 

4  -2977.8  2979.6 

5  -2981  5  2983.3 
G  2985.2  2987.0 

-2988.9  2990.7 
8  -2992,6  2994.4 
,  •29%.3  2998.1 
810  3000.0  3001  8 

3003.7  3005.6 

3007.4  3009.3 
3011.1  3013  0 

3014.8  3016.7 

3018.5  3020.4 

6  3022.2  3024.1 

3025.9  3027.8 

8  3029.6  3031.5 

3033.3  3035.2 

3037.0  3038.9 

3040.7  3042.6 

3044.4  3046.3 

3048.1  3050.0 
3051.9  3053.7 
3055.0  3057.4 
3059.3  3001.1 
3003.0  3004.8 
3066  7  3068.5 

9  3070.4  3072.2 
83  0  3074.1  3075.9 

3077.8  3079.6 
3081.63083.3 
3085.2'3087.0 
30:i8.9'3090.7 

3092.6  3094.4 
3096.3  3098.1 
3100.0  3101.8 

8  3103.7  3105.0 


84(J 
1 


8  3140. 

9  3144.4 
85  0  3148.1 


3109.3 
3113.0 
3110.7 
3120.4 
31-24.1 


9  3107.4 
3111.1 
3114.8 

2  3118.5 

3  3122.2 

4  3125.9  3127.8 

5  31-29.6  3131.5 

6  3133  3  3135.2 

7  3137.0  3138.9 
3142,6 
3140.3 
3150.0 

1  3151.9  3153.7 

2  3165.0  3157.4 

3  3159.3  3101.1 

4  3103.0  3164.8 
6  3166.7  3168.5 

6  3170.4  3172.2 

7  3174.1  3176.9 

8  3177.8  3179.0 
93181.631833 

3185.2  3187.0 

1  3188,9  3190.7 

2  3192.6  3194.4 

3  3196.3  3'98.1 

4  3200.0  3201.8 
6  3203.7  3205.6 

6  3207.4  3209.3 

7  3211.l'3213.0 

8  3214.8|3216  7 

9  3218.5  3-220.4 
870  322-2.2  3-224.1 

1  3225,9  3-2-27.8 

2  32.9,6  3-231.5 

3  3233.3  3235.2 

4  3237.0  3238,9 
6  3240  7  3-242.6 

6  3244.4  3246.3 

7  3248.1  3-250.0 

8  3251.9  3253.7 

9  3-255.6  3257.4 
88  0  3259.3  3261.1 

1  3263.0  3264.8 

2  3266.7  3268.5 
8  3270.4  3272.2 
4^3274. 1  3275.9 
6 13-277.8  3279.6 

6  3281.5  3283.3 

7  3285.2  3-287.0 

8  3288.9  3290.7 

9  329-2.6  3294,4 
890  3296.3  3-298.1 

3300.0  3301.8 

3303.7  3305.6 

3  3307.4  3309.3 

3311.1  3313.0 

3314.8  3816.7 
.3318.5  3320.4 

7  33-2-2.2  3324.1 

8  33z5.9  3327.8 

9  3329.6  3331.6 
900  3333.3  3335.2 


] 

2 
3 
4 
5 
6 
7 
8 
9 

910 
1 
2 

3 
4 
5 
6 
7 
8 
9 

920 
1 
2 


Contents, 
Cn.  Yds. 


900  3333.3  3335,2 
3337.0  3338.9 

3340.7  3342.6 

3344.4  3346.3 
3348.1 .33.50,0 
3351.9  33.53.7 
3355.6  3357.4 
3359.3  3361.1 
3363.0  3364.8 

9  3366.7  3368.5 
3370  4  3372.2 
3374.1 '3375.9 
3377.8'3379.6 

3381.5  3383.3 

3385.2  33x7.0 
3383.9  3390.7 

6  3392.6  3394.4 

3396.3  3398.1 

3400.0  3401.8 
9  3403  7  3405.6 

.3407.4  3409.8 

3411.1  3413.0 

3414.8  3416.7 
313418  5  3420.4 

4  ;3422.2  34'24.1 

5  3425.9  3427.8 

6  3429.6  343  i  .5 

7  3433.3  3435.2 

8  3437.0  3438.9 

9  3440.7  3442.6 
93  0  3  444.4  3446.3 

1  3448.1  3450.0 

2  3451.9  3453.7 

3  3455.6  3457.4 

4  3459.3  3401.1 
6  3463.013404.8 
6  3460.7  3468.5 
7,3470.4,3472.2, 

8  3474.1  3475.9 

9  3477.8  3479.0 
940  3481.6  3483.3 

1|3485.2'3 187.0 

2  3488.9  3490.7 

3  3492.03494  4 

4  3490.3  3498.1 
5j3500.0'3501.8 
6  3503.7  3505.6 
7 13507.4  3509.3 

8  3511.r3513.0 

9  3514,8  3510.7 
950  3518.6  3520.4 

1  3522.23524.1 
3525.9|3527.8 
3  3529.0  3531.5 
43533.3  3-535.2 
6  3537.0  3.5,38-9 

6  3540.7  3542.6 

7  3544.4  3546-3 

8  3548.1  3550.0 
9,3551.9  3553,7 

960  35-55.6  3557.4 
1'3559.3  3561  1 
2'3563.0  3.564  8 

3  3560.7  ,3568.5 

4  3570.4  3572  2 
6  3574.1  3575  9 

6  3577.8  3579.0 

7  3581.5  3.583.3 

8  3585.2  3587.0 

9  3-588.9  3590.7 
970  359-2.6  3.594.4 

1  3596.3  3698.1 

2  3000.0  3601.8 
8  3603.7  3005.6 

4  3607.4  3609.3 

5  3611.1  3613.0 

6  3614.8  3010.7 

7  3618.5  3020.4 

8  3622.2  3624. 1 

9  3625.9  3627.8 
980  36-29.0  3631.5 

1  3633.3  3035.2 

2  3637.0  3638.9 
8  3640.7  3642  6 
4  3044.4  3()40  3 
6  3648.1  3650.0 

6  3651.9  3053.7 

7  3065.0  3057.4 

8  3059.3  3601.1 

9  3603.0  3664.8 
990  3666.7  3668.5 

1  3670.4  367-2.2 

2  3674.1  3675.9 

3  3677.8  3679.6 

4  3681.5  3683  3 
6  3685.2  3687.0 

6  3688.9  3690.7 

7  3692.6  3694.4 

8  3696.3  3698.1 

9  3700.0  3701.8 
1000  3703.71 


\ 


RATIOS  OF  CORRECTION  FOR  AVERAGE  EB^D  AREA  CALCULATIONS. 


WIDTH  OF 
UOAI)  UEO. 


AiTa  of 
Sdi  n  Knd. 


1.25    2  2.5 


H  i^'ht  III 
Siii  'il  KikI, 


I  lia  io  i>r 
I  V.ml 
Ai'cns. 


1:1 

1:1. -2 

1:1.4 

1:1. (i 

1:1. S 

1:2 

1:2.5 

1::{ 

U-.l.o 

1:1 

1:4.5 

1:5 

1:  ..5 

1:(> 

1:(!.5 

1:7 

1:7.5 

1:S 

1:^5 

1:I> 

1::».5 

1:10 


S«*i-t<011 

Vill  i  ills 
I II  a  1 
SI'  es. 


.001 
.UU2 
.007 
.012 
.019 
.0.",3 
.Oio 
.056 
.01)7 
.076 
.()S5 
.O'j:^ 
.100 
.107 
.113 
.119 
.124 
.l--'8 
.133 
.13S 
.142 


1     1  1 


Slope. 


(Mil 

oo;; 

006' 
iilO 
OH 
023 
1132 


1:1 

001' 
.004 
.007 
.012 
.018 
.032 
.043 


(111  .O'lo 
050  .060 


057 
065 
071 
077 
083 


,075 
.083 
.091! 
.098' 
105 


089j.ll0 
094  .115' 
lOol.ll'O 


1 06 
111 
117 
123 


.125'. 
.130. 
.134  . 
.138. 


1J:1 

.001 
.004 
.OON 
.012 
.0 

.033 
.044 
,056 
.067 
.076 
.084 
.092 
.100 
.106 
.111 
.116 
.122 
.127 
132 
1 36 
140 


2-12 


2.25   to  100 


14 


100 


1—5 


Slope. 


6.04  5.2  4.74 


Slope. 


16 


18 


100 


74  4.81  4.41 


Slope. 


1-1 

4  •  ^ 


001 
002 
.001 
006 
'Jo9 
016 
023 
.030 
.ii3S 
,043 
049 
,0.55 
060 
1)65 
O70 
075 
079 
084 
OSS 
092 
097 


1:1 

.001 
.004 
.006 
010 
.014 
;026 
037 
.047 
.057 
,066 
.074 
,081 
,088 
,094 
,100 
105 
110 
115 
120 
125, 
130 


1.1:1 


.001 

,004 

,007 

,011 

,015 

,027 

040 

051 

,061 

070 

07  S 

084 

09, 

099 

105 

110 

115 

120 

125 

130 

135 


i-.l 


.001 
.002 
.003 
.005 
.006 
012 
,019 
.026 
.033 
.039 
.044 
.050 
.055 


1:1 


.001 
.003 
.006 
.010 
.014 


.001 
.003 
.006 
.010 
.014 


.024.021 


037 
047 
056 
065 


035 
045 
054 
062 

.0701.07 
0771.030 
084. OSS 
060  .090'  095 
065^.095  .101 
069.100i.105 
073, .106'. Ill 


,077  111 
0821,116 
086. 121 
090'.126: 


.116 
.121 
.125 
.130 


J:l 


.001 
.002 
.003 
.005 
.010 
.016 


1:1 


.001 
.003 
.006 
.010 
.014 
.024 
.033 


.022  .042 
.029  .051 
.035 
.040 
.046 


001 
003 
006 
010 
.014 
025 
035 
.047 
.054 


.059  .062 
.066  .070 
.073  .078 
.051  .079  .085 
.056  .085  .091 
.060  .0911.097 
,004.09'i'.102 
,068  .101  .107 
.072  .106  .112 
076  .1111.117 
086  .116'. 121 
084  .120  .126 


100 


•5.14  4.45  4.13  4.72  4.14  3.88  4.33  3.87  3.644.00  3.62  3.4; 


Slope. 


1-1 

4.1 


1:1  1J:1 


.001 
.002 
,003 
,005 
010 
,014 
,020 
025 
031 
036 
042 
047 
051 
055 
058 
062 
065 
069 
072 


.001 
.003 
.006 
.009 
.013 
.022 
.031 
.039 
.048 
,055 
003 
070 
.076 
.082 
.088 
.093 
.098 
.102 
.106 
111 


0751.116 


.001 

.003 
.006 
.009 
.013 
.021 
.034 
,044 
,052 
,060 
,068 
,075 
082 
,088 
093 
098 
103 
108 
113 
117 
122 


20 


100 


Slope. 


1.1 

4.1 


001 
.002 

003 

005 
.010 
.014 
.019 
.02* 
.028 
.033 
.037 
.041 
.045 
.049 
.053 

056 1 
.0(iO| 
.063: 
,066j 
.069! 


.001  .001 
.003  .003 
.005  .005 
.008  .009 
.012.013 
.020  .023 
.028  .033 
.037  .042 
045  .050 
.053  .058 
060,.066 
.066. 073 
.072  .079 
.078  .085 
.083  .090 
.088  .095 
.093  .100 
.097  .104 
.102  .109 
,106  .113 
.111'. 118 


100 


24 


100 


Slope. 


Slope. 


1:1 


U:l 


 '.001 

0011.003 
002'.005 
003  .007 
OO5LOI] 
009  .019 


,014 
,019 
,022 
026 
030 
034 
037 
041 
044 
047 
050 
054 
057 
060 
063 


-026 
.034 
.042 
.049 
.056 
.062 
.06,> 
.074 
079 
.084 
.089 
.094 
.098 
.103 
.107 


.001 
.003 
.005 
.00,s 
.013 
.021 
.030 
0!9 
.047 
.055 
.062 
069 
.075 
.081 
.086 
.091 
.095 
.100 
,105 
.110 
.114 


1-1 
4.1 


001 
.002 

.ro3 

.005 
,010 
,013 
,017 
021 
024 
,028 
,031 
034 
037 
.040 
043 
047 
050 
.053 
056 
059 


U:l 

.001 
.003 
.005 
00- 
012 
020 
02« 


1:1 

.001 
.003 
.005 
.007 
.010 
.017 
.025 

.0321.036 
.045 
.052 
.059 
.066 
.07 
.077 
.082 
.0s7 
.092 
.097 
.lol 
.lOi- 

,110 


.039 
.046 
.053 
.059 
.064 
.070 
.075 
.080 
,084 
OSS 
.093 
.098 
,102 


2G 


28 


100 


100 


30 


100 


!.71  3.43  3.2413.47  3.20  3.07  3.24  3.20  2.91 


Slope. 


l-.l 


001 
.002 

,003 
005 
,008 
012 
016 
0i9 
022 
025 
()28 
031 
034 
037 
040 
043 
046 
048 
051 


1:1 


.001 
.002 
.004 
.O0( 
009 
016 
.023 
.030 
.037 
.044 
.050 
055 
.060 
065 
.070 
075 
080 
084 
088 
.093 


••54  .097 


U:] 


.001 
.003 
.005 
.008 
.011 
019 
.027 
.034 
.042 
05(1 
057 
063 
0(i9 
075 
.OKO 
085 
0s9 
094 
098 
.10-.' 
107 


Slope. 


J:l'  1:1  1J:1 


.001  .001 
.002  .002 
.001  .005 
.006.007 
.009  .010 
.015  .018 
.022  .025 
.029  .033 
.035  .040 
.041  .04S 
.018  .054 
.053  .060 


001 
001 
,002 
003 
,006 
010 
013 
016 
019 
022 
025 
027 
030 
033 
036 
OSS 
041 
044 
046 
049 


.058 
.063 
06 


.06fi 
072 
,077 


.O72L082 
.076  ,086 
.080.091 
.084  .09  ") 
.088  ,100 
.092  .104 


Slope. 


4 


,001 

001 
,002 
O03 
005 
008 
Oil 
014 
.016 
.019 
021 


I 

1:1  1!:1 


.001  .001 
.002  .(J0-' 
.004  .005 
.006  .007 
.008  .010 
.014.017 
021  .024 
.027  .('32 
.034  .030 
.040  04(; 
045  .052 
.050  .058 
024  .0.55  064 
.|'26  .0(30  .0(;9 
029  .064  .074 
031  .068  079 
.034  .072  .084 
036  .076  ,0.-<8 
039  .(/79  .092 
041  .083  .09() 
044  087  .100 


ll:i1ioof 

Ktnl 
Areas. 


1:1 

1:1.2 

1:1.4 

1:1. « 

1:1. i» 

1:2 

1:2.5 

l::j 

l::j.5 

1:4 

1:4.5 

1:.> 

i:"-.o 

l:<i 

l:<;.5 

1:7 

1:7.5 

l:S 

1:^.5 

l:!t 

1:!).5 


On  Estimating  Earthwork. 

The  accompanying  table  is  cle.signefl  to 
facilitate  the  computation  of  eartlnvurk 
after  the  areas  of  the  cross  sections  have 
b(^en  (ihtaiiied.  The  areas  may  be  ob- 
taioefl  by  calciilatiim  from  the  field  notes  ; 
or  the  cross  sections  may  be  plotted  and 
the  arf-as  obtained  by  the  piani meter. 
The  farmer  method  is  short  and  easy  in 
a  level  country,  but  where  the  surface  of 
the  griuuid  is  broken  and  irregular  the 
latter  method  is  to  be  preferred.  Plotting 
the  cross  s 'ctions  also  makes  a  complete 
record  of  the  work,  with  its  classification 
at  every  point,  and  allows  revision  and 
deviation  within  the  limits  to  which  the 
section  is  taken,  by  simply  indicating  the 
position  of  the  centre  line.  Usua'ly  it 
will  be  found  easiest  to  plot  the  rods 
from  a  line  a.-^siimed  as  the  height  of  in- 
strument; but  when  the  work  is  extend- 
ed so  as  to  involve  several  heights  of 
instrument  in  the  same  section,  or  .vhen 
the  work  is  to  be  used  for  a  great  i, ember 
of  calculations  for  successive  estimates, 
it  will  be  found  cheapest  to  work  from 
elevations. 

A  cmvtnient  form  for  the  estimate 
sheets  is  here  shown.  In  the  two  first 
columns  ar<^  entered  the  stations  and 
plut-es  at  which  the  cross  sections  are 
t:iken.  The  column  headed  "Length  in 
Feet"  is  filled  up  by  bubtracting  the 
numbers  in  these  two  first  columns.  The 
columns  headed  "  Area  uf  Gross  Section  " 
are  fiihd  up  with  areas  obtained  either 
fiom  calculation  or  from  measurement 
by  the  planimeter.  In  the  columns  head- 
ed ''Average  Area"  are  eut*;red  one-half 
the  sums  of  the  areas  of  adjacent  cross 
sections.  If  preferred  the  sums,  in.-tead 
of  the  half  sums,  may  be  used,  in  which 
case  the  final  contents  will  be  doubled. 

The  main  columns  of  "  Coiitenta  in 
Cubic  Yurd-i^'  are  now  filled  up  by  aid 
of  accompanying  "  Table  of  Cubic  Yards 
in  Lengths  of  100  Feet"  If  the  lengths 
are  K'O  feet  the  corresponding  quantities 
are  sim|)ly  transfeired  fVom  the  table.  If 
the  distance  is  50  feet,  one  half  the  quan- 
tity is  transferreil.  If  the  distance  is  25 
feet,  one-fi)urth,  &c.  Usually  the  opera- 
tion can  be  })erfbrmed  mentally.  The 
table  being  set  u[)  before  one,  the  arrange- 
ment of  it  is  such  that  the  eye  knows  just 
where  to  strike  for  a  quantity.  There 
are  no  leaves  to  turn.  Quantities  can  be 
entered  as  fast  as  one  can  write.  Blue 
ink  may  be  used  in  writing  quantities  in 
excavation,  and  red  ink  in  writing  quan- 
tities in  embankment. 

The  calculation  of  earthwork  by  the 
mt^thod  of  averaging  end  areas  is  not 
theoretically  correct,  excepting  in  the 
two  special  cases :   one  when  the  end 


areas  are  equal,  and  the  other  wlien  the 
prismold  has  two  of  its  longitudinal 
bounding  planes  ]iarallel.  As  that  por- 
tion of  every  roadway  prismoid,  wdiich 
lies  between  the  vertical  planes  passing 
through  the  edges  of  the  roadbed  is 
practically  included  in  the  latter  comli- 
tion,  it  fijilows  that  the  variation  from 
the  true  contents,  obtained  from  averag- 
ing end  areas,  lies  outside  the  central 
roadbeil  prism,  and  we  may  consider  it  as 
dependent  on  the  four  following  factors : 

1st.  The  ratio  of  the  end  areas  of  the 
prismoid. 

2nd.    The  width  of  the  roadbed. 
3rd.    The  degree  of  the  slope. 
4th.    The  heighth  of  the  section. 

This  variation  has  been  investigated 
with  the  result  shown  in  the  table  called 
"Ratios  of  Correction  for  Average  Fnd 
Area  Calcidations."  The  manner  of  pro- 
ceeding was  briefly  thus :  With  the  data 
shown  in  the  heads  of  the  columns  in 
the  table,  and  in  the  left  hand  column, 
the  true  contents  of  the  prisms  by  the 
prismoidal  formula  were  found,  as  well 
as  the  contents,  by  averaging  end  areas. 
The  ratio  of  variation  in  many  par- 
ticular cases  being  thus  found,  the  curve 
of  variation  for  each  class  was  formed 
by  measuring  the  ratios  of  end  areas 
on  the  axis  of  abscissas,  and  the  per- 
centages of  variation  on  the  axis  of  ordin- 
ates.  Some  maxima  and  minima  of  these 
curves  were  also  traced,  which  seemed 
to  differ,  in  extreme  cases,  10  per  cent,  or 
so  from  the  mean  given  in  the  table.  It 
is  believed  the>e  deviations  will  usually 
counterbalance  one  another.  If  the  work 
is  of  a  peculiar  nature,  so  the  general 
cases  here  w,>rked  out  will  not  apply,  cor- 
rections applying  to  it  can  be  worked  out 
and  entered  in  one  of  the  blank  columns. 

To  apply  the  table  of  corrections,  we 
divide  one  area  of  cross  section  by  its 
neiglibor,  and  take  from  the  table  its  cor- 
responding ratio  or  percentage  of  correc- 
tion and  multiply  the  contents  by  it, 
writing  the  result  in  the  column  headed 
"  Correction"  The  special  case,  when 
one  end  is  zero,  or  ends  at  grade,  is  not 
provided  fi)r  in  table  of  corrections.  For 
this  case  the  correction  is,  the  slope  area 
multiplied  by  one  sixth  the  length.  F(;r 
the  road  bed  area  being  the  base  of  a 
wedge,  the  solidity  is  one-half  base  multi- 
plied by  altitude;  but  the  slope  areas  being 
bases  of  pyramids,  the  solidity  is  one-third 
base  multiplied  by  altitude.  One  half 
which  is  used,  less  one-third,  wdiich 
should  be  used,  equals  the  correction,  cue- 
sixth.  This  correction,  as  well  as  all 
others,  is  to  be  deducted  from  contents  in 
main  column. 


Estimated  Q,nantities  in  Grading. 


STA- 


No. 


AHKA  OF  CROSS 

-VX.  ION 
IN  S({U»1£K  ^T. 


KxcaT.it  ion. 

-  Em. 

1  i  iiieiit 


11 

118 

'iiV) 


120 


121 


123 


50  mt  com 

....I  18.  16 

50158  53105 
....()3(.)163325 


50  638  2635 
85417j297 


,...!ll02434S5 


ends 


20  cat! 
40  Cut  com  men  cesos 
no;  31 

80103 
....'334280 
35700  277  5.55 
.5074315 


12250870156  209 


..821 

50534 
Hlj  cut 
70 
84 

tlO 


1*^7 


ends 


AVERACE  AREA. 


Excavation. 


!iiec'ces 

30  


560 
555 
314 


3147 


.394 
....  634 

....527. 

2(;3 
55 


It  coimen'ces 


15i 
72 

■im 

517" 
521 J 
806.1 
845,? 
67  7  r! 
267 


34 
108 
212 
280 
270 
121. 


170 
27  8  i 
217 
156.', 
171,5 
130 
36i 


15 

67^ 
215,! 
426 
560.1 
540 
■2i-l\ 


280 
557^ 
434. 
26 1.^ 
232 
201 
73.', 


Em- 

h.<nk 
111  en  t 


23 
46 
23 


50 
50 
50 
50 
35 
15 
20 
20 
20 
20 
20 
35 
15 
100 
50 
30 
31 

9 
14 

6 


Corrected  Totals, 


CONTtNTS  IN  tUBtC  YARDS. 


Excavation. 


16.7  1 
162.916 
729.632 
1174.1 
683.8 
136  3 
40.7 


11.4 

53.3 

161.9 

670.:: 

400  S 
2987.0 
1565 

752.8 

306.518 


9,s53.7  98 


9755.7!. 


14  8 
63.9 
200,6 
394  4 
302.9 
150  0 
90.0 


103  7 
361.0 
120  6 
579  6 
317.(1 
144.4 
41.9 


2945.423 


27 
125.0 
399. 
788.9 
626,5 
300.0 
179.6 


207.4 
722.7 
241.3 
96.S.5 
429  6 
223.3 
84.4 


2922.4!....  5278.1  ....i  82.7....! 


Ein- 
(•aiil,. 
nil  III. 


25  1 
25.1 


/.6 

23.8 
5.1 


12414(31  86.- 


REMARKS. 


The  error  from  calculation  by  averag- 
ing end  areas  is  not  so  great  as  appears 
at  first  sight,  or  as  it  is  often  represented. 
Taking  isolated  cases,  where  the  ratio  of 
end  areas  is  great,  it  may  be  made  to 
appear  that  the  error  is  10  or  15  per  cent.; 
but  taking  extended  work  the  whole 
error  is  trifling,  the  great  bulk  of  con- 
secutive cross  sections  being  nearly  equal 
to  each  other,  and  the  err(n-s  are  distri- 
buted. The  writer  tested  one  section  of 
28,(,0  >  cu.  yds.  and  f  lund  the  error  less 
than  one  third  of  one  per  cent.  What 
appeared  to  be  a  section  which  would 
show  great  error  on  account  of  crossing 
several  short  ravines  and  gullies,  con- 
taining some  85.000  cu.  yds.,  was  less  than 
onedialf  of  one  per  cent,  out  of  the  way. 

In  earthwork  there  are  only  two  sides 
of  the  prismoid  perfect  planes,  and  these 
two  are  the  theoretical  ])lanes  of  the 
cross  section.  The  surface  of  the  ground 
is  never  a  perfect  plane.  The  rod,  in 
taking  points  usually  siok<  a  little  in  the 
grounil,  the  slopes  are  not  trimmed  exact- 
ly, nor  the  grade  made  perf<  ct.  If  there 
is  any  difierence  between  the  true  so'idity 
and  that  obtained  by  the  method  here 
presented,  it  is  the  conviction  of  the 
writer  that  it  would  be  easier  and  chea[)- 
er  f  >r  the  engineer  to  shovel  it  than  to 
calculate  it. 

The  method  of  calculation  for  earth- 
work should  be  direct  and  simple,  so  it 
can  be  used  safely  by  assistants  not  speci- 


ally skilled  in  intricate  calculations.  It 
is  better  for  the  engineer  to  spend  much 
of  his  time  in  the  field,  minutely  observ- 
ing ;xnd  closely  measuring  the  work,  than 
to  spend  it  mainly  in  the  office,  basing 
refiued  computations  on  erroneous  or 
careless  measurements.  The  errors  in 
measurement  will  usually  be  greater  than 
the  errors  of  calcuhition,  by  averaging 
end  ;irea.s  without  correction. 


— Publislied  by— 

JOHN  WILEY  &  SONS, 
^eieiitific*Ir*«l>li»lier^ 


15  Astor  Place. 


NEW  YORK  CITY. 


The  New  and  Complete  Catalogue 

.^OF_THE  PUBT^ICATIONS  OF 

,rOH]\WIL.EY  &  SOIVS, 

IS  Astor  Place,  New  "York, 
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TABLE  OF  CUBIC  YARDS  IN  LENGTHS  OF  100  FEET. 

ADAPTED  ESPECIALLY  TO  THE  CALCULATION  OF  EARTH  WORK  BY  THE  METHOD  OF  AVERAGING  END  AREAS. 


Contents  of  Column  "A"  are  for  the  integers  in  column  headed  "Area,  Square  Feet." 
Contentsi  of  Column  "  B  "  are  for  tlie  same  integers  plus  0.5  square  foot. 


Contents  for  lengths  greater  or  less  than  100  are  obtained  by  simple  proportion,  thus  :  125 
sq.  ft.  for  length  of  20  ft.=i%=5  of  463.0  cu.  yds;  the  contents  for  125  sq.  ft.=92.6  cu.  yds. 


COPYRIGHT  IS8S  BY  S.  B.  FISHER. 


Contf-pts, 

Couteiits, 

Cuiiteiiis,  1 

at  itt 

Cu.  Yds. 

U  i. 

<V1 

Cu.  Yds. 

Cm.  Yds.  j 

A. 

B. 

A. 

B. 

U  • 

A. 

B. 

1  s 

370.4 

372.2 

200 

740.7 

742.6 

J 

3.7 

5.6 

1 

374.1 

375.9 

1 

744.4 

746.3 

a 
Z 

Q  ^ 
y  .o 

» 

377.8 

379.6 

2 

748  1 

7-)0  0 

o 
o 

111 

13  0 

9 
O 

381.5 

383.3 

3 

751.9 

753.7 

A 

14.8 

1  r>  7 

A 

385  2 

387.0 

4 

755.6 

757.4 

e 
O 

18.0 

20.4 

O 

388.9 

390.7 

5 

759.3 

761.1 

o 

22.2 

24.1 

a 
o 

39i.6 

394.4 

6 

763  0 

764.8 

7 

2,s  9 

97  K 

396  3 

393.1 

7 

766  7 

768.5 

c 
r* 

29.6 

31.5 

g 

400.0 

401.8 

8 

770.4 

772  2 

o 

33  3 

35.2 

9 

403.7 

405.6 

9 

774  1 

775.9 

1  i\ 

lU 

37.0 

38.9 

110 

407.4 

409.3 

21<» 

777.8 

779.6 

1 
J 

40.7 

42.6 

411.1 

413.0 

1 

781.5 

783.3 

a 

44.4 

46.3 

2 

414.8 

416.7 

2 

735-2 

787.0 

Q 

48.1 

50  0 

9 
o 

418  5 

420.4 

3 

788-9 

790.7 

A 

51.9 

53-7 

4 

422  2 

421.1 

4 

792.6 

794.4 

K 

o 

55.6 

57.4 

425.9 

427.8 

5 

796-3 

798.1 

a 
o 

59.3 

61.1 

429  6 

431.5 

G 

800.0 

801.8 

i 

63.0 

64  8 

7 
• 

433  3 

435.2 

7 

803.7 

805.6 

fi 

o 

66.7 

68.5 

g 

437.0 

438  9 

g 

807.4 

809.3 

Ik 

«F 

70.4 

72  2 

9 

440  7 

442.6 

9 

811.1 

813.0 

74.1 

75.9 

120 

414.4 

416.3 

220 

814.8 

8167 

1 

X 

77.8 

79.6 

] 

448  1 

4-50.0 

1 

818.5 

820-4 

O 
u 

a 

81.5 

83.3 

2 

451.9 

453.7 

2 

822  2 

824  1 

85.2 

87.0 

3 

455.6 

457.4 

3 

825,9 

827-8 

A 
* 

88.9 

90.7 

A 

459  3 

461.1 

4 

829.6 

831-5 

w 

92  6 

94.4 

463.0 

464-8 

f. 

833.3 

835.2 

n 

96.3 

98.1 

(} 

466.7 

468.5 

G 

837.0 

838.9 

i 

loo  0 

1018 

7 

470.4 

472.2 

7 

840.7 

842.6 

c 

o 

103.7 

105.6 

g 

474.1 

475.9 

8 

844.4 

8463 

9 

107.4 

109.3 

9 

477.8 

479.6 

9 

843-1 

850-0 

30 

HLl 

113.0 

130 

481.5 

4833 

230 

851-9 

853-7 

\ 

1 14.8 

116.: 

1 

485.2 

437.0 

1 

85-5.6 

857-4 

2 

120.4 

2 

488.9 

490  7 

2 

8.59.3 

861.1 

122.2 

124.1 

3 

492.6 

494.4 

8 

863.0 

864.8 

4 

125.9 

127.8 

4 

496.3 

493.1 

4 

8637 

863  5 

5 

129'6 

131.5 

5 

500.0 

501.8 

5 

870  4 

872  2 

133.3 

135.2 

0 

503.7 

505.6 

G 

874.1 

875-9 

l37!o 

133  9 

7 

507.4 

5(19.3 

7 

877.8 

879-6 

g 

140.7 

142.6 

g 

511.1 

513.0 

8 

881.5 

833.3 

9 

144.4 

143.3 

9 

514.8 

516.7 

9 

835.2 

887-0 

40 

143  1 

150.0 

14o 

518.5 

520.4 

240 

883  9 

8907 

1 

151.9 

153.7 

1 

522  2 

524.1 

1 

802-6 

89 1.4 

2 

1 5o.6 

157^4 

2 

525.9 

527.8 

2 

803.3 

893.1 

3 

loois 

161.1 

3 

529.6 

531.5 

8 

900  0 

901.8 

4 

103  0 

164.8 

4 

533.3 

535.2 

4 

903-7 

91 '5.6 

1637 

163.5 

5 

537  0 

533.9 

5 

937.4 

909.3 

170.4 

172.2 

540.7 

542.6 

G 

911.1 

913.0 

7 

g 

I74!l 

175.9 

7 

544.4 

546.3 

7 

914.8 

916.7 

177.8 

179.6 

g 

543.1 

550.0 

g 

918.5 

920.4 

9 

13L5 

183  3 

9 

531.9 

553.7 

9 

922  2 

924.1 

50 

135.2 

187.0 

15o 

555.6 

557.4 

250 

92)  9 

927.8 

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138.9 

1907 

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559  3 

531.1 

1 

920.6 

931.5 

2 

ll)2'6 

191.4 

2 

563.0 

534.8 

2 

933.3 

935.2 

3 

193.3 

193.1 

3 

566  7 

563.5 

3 

937.0 

933.9 

4 

200.0 

201^8 

4 

570.4 

572  2 

4 

94).7 

942.6 

5 

203.7 

205.6 

5 

574.1 

575.9 

5 

914-4 

946-3 

c 

2J7!4 

209^3 

({ 

577.8 

579.6 

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918.1 

950.0 

2!  1.1 

213.0 

581.5 

683.3 

7 

951-9 

953.7 

g 

214!8 

2167 

g 

585.2 

587.0 

8 

955  6 

9-57,4 

9 

218.5 

220.4 

9 

538.9 

590.7 

9 

959.3 

961.1 

GO 

222  2 

224.1 

160 

592  6 

594  4 

260 

933-0 

964.8 

1 

225  9 

227.8 

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596  3 

598.1 

1 

9307 

968.5 

2 

229.6 

231.5 

2 

600.0 

601.8 

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970  4 

972.2 

3 

233.3 

235.2 

3 

603  7 

605  6 

3 

974.1 

975.9 

4 

237.0 

238^9 

4 

007.4 

609.3 

4 

977.8 

979.6 

5 

210  7 

242.6 

5 

611.1 

613.0 

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931.5 

983.3 

244.4 

246.3 

614.8 

616.7 

6 

985.2 

987.0 

7 

248.1 

250.0 

7 

618.5 

020.4 

7 

988  9 

990.7 

g 

251.9 

253.7 

g 

622.2 

624  I 

8 

992-6 

994-4 

9 

2'>5.6 

257.4 

9 

625  9 

627.8 

9 

996-3 

998  1 

70 

259.3 

231.1 

17u 

629.6 

631.5 

27it  1000-0  1001.8 

1 

2')3  0 

264.8 

1 

633.3 

635.2 

1  10037  1005.6 

2 

2G6  7 

263.5 

5; 

637.0 

638.9 

2  1007  4  1009.3 

270.4 

272.2 

3 

640  7 

642.6 

3  1011.1  1013-0 

4 

274.1 

275.9 

4 

644  4 

640.3 

4  1014-8  10167 

5 

277.8 

279.6 

5 

648  1 

650.0 

ft  1018-5  1020.4 

( 

281.5 

283.3 

(; 

651  9 

653. 

6  1022.2  1024.1 

7 

285.2 

237.0 

7 

655  6 

657.4 

7  1025.9  1027.8 

g 

288.9 

290.7 

g 

6')9.3 

661  1 

8  1029.6  1031.5 

<) 

2926 

294.4 

9 

663  0 

664.8 

9  10-33.3  103.5.2 

g(l 

296  S 

298.1 

180 

636.7 

608.5 

280  1037.0  1038.9 

1 

300.(: 

301.8 

) 

670.4 

672.2 

1  1040.7  1042.6 

2 

3i)3.'7 

30)!6 

2 

674  1 

675.9 

2  1044.4  1046  3 

g 

307.4 

309.3 

3 

677.8 

679.6 

3  1048.1  1050-0 

4 

311.1 

313.0 

4 

631  5 

683.3 

4  1051.9  1053.7 

h 

314.8 

3167 

5 

6852 

687.0 

6  1055.6  1057.4 

G 

318.5 

320.4 

6 

688.9 

690.7 

6  1059  3  1061.1 

7 

322.2 

324  1 

7 

692.6 

694.4 

7  1063-0  1064.8 

8 

325.9 

327.8 

8 

696.3 

698.1 

8  1066  7  1068.5 

9 

329,6 

331.5 

9 

700.0 

701.8 

9  1070.4  1072.2 

90 

333.3 

335.2 

190 

703.7 

705.6 

29i(  1074.1 

1075.9 

1 

337. u 

338.9 

1 

707.4 

709.3 

1,1077.8 

1079.6 

2 

340.7 

342.6 

2 

711.1 

713-0 

2  1081-5 

1083.3 

3 

344.4 

346.3 

8 

714.8 

716.7 

3 

1085.2 

1087.0 

4 

318  1 

350.0 

4 

718.5 

"^20.4 

4 

1088.9 

1090.7 

o 

351.9 

353.7 

722.2 

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5 

1092-6 

1094.4 

6 

3-)5.6 

357,4 

6 

725.9 

727.8 

G 

1096.3 

1098.1 

7 

359.3 

361.1 

7 

729  6 

731.5 

7 

1100.0 

1101.8 

8 

363.0 

364.8 

8 

733  3 

735.2 

8 

1103.7 

1105.6 

9 

366.7 

368.5 

9 

737.0 

738-9 

9 

1107.4 

1109.3 

IOC 

S70.4 

372.2 

200 

740.7 

742.6 

300 

1111.1 

1113.0 

300 
1 
2 
3 
4 
6 
6 
7 
8 
9 

310 
1 
2 
3 
4 
5 


Coiiti'iiis, 
Cu.  Yd.s. 


A. 


1111.1  1113.0 
1114.8  1 1167 


9 

320 
] 
2 
3 
4 
6 
6 
7 
8 
9 

380 
1 
2 
3 
4 
5 
G 
7 
8 
9 

340 
I 


1118.5 
1122.2 
112-5.9 
1129.6 
113.3.3 
1137.0 
1140.7 
1144.4 
11481 
1151.9 
1155  6 
1159  3 
1163.0 
1166.7 
1170.4 
1174.1 
1177.8 
1181.5 
1185-2 
1188  9 
1192-6 
1196.3 
1200  0 
1203.7 
1207.4 
1211.1 
1214.8 
1218  5 
1222.2 
1225  9 
1229-6 
1233-3 
1237-0 
12407 
1244.4 
1248  1 
1251.9 
1255-6 
1259-3 


1120-4 
1124.1 
1127S 
1131.5 
113-5.2 
1133.9 
1142-'! 
1146-3 
11.50-(i 
1 153  7 
1157.4 
1161.1 
1164.8 
1168-5 
1172.2 
1175  9 
1179.6 
11833 
1187.0 
11907 
11944 
1198.1 
1201.8 
1205.6 
1209.3 
1213.0 
1216.7 
1220.4 
1224.1 
1227.8 
1231.5 
1235.2 
1238.0 
1242.6 
1216.3 
12-50  0 
1253-7 
1257.4 
1261-1 


(  ontents, 
Cm..  Yds. 


1233.0  1264  8 


1266.7 
1270.4 
4' 1274.1 


1 

2 
3 
4 
5 
6 
7 
8 
9 

360 
1 
2 
3 
4 
5 
6 
7 
8 
9 

370 
1 

2 
8 


6 
7 
8 
9 

380 
1 
2 
3 
4 
5 
G 
7 
8 
9 

390 
1 
2 
3 
4 
5 
G 
7 
8 
9 


1277.8 
1231.5 
1235.2 
1283.9 
1.92-6 
1296.3 
1300.0 
13037 
1307-4 
1311.1 
1314-8 
1318-5 
1322  2 
1325-9 
1329.6 
13333 
1337.0 
1340.7 
1344.4 
1348.1 
1351.9 
135-5-6 
1359-3 
1363-0 
1366.7 
1370.4 
1374.1 
1377.8 
1381-5 
1385.2 
1388.9 
1392.6 


268 
1272.- 
1275.9 
1279  6 
1233.3 
1287.0 

1290-  7 

1291-  4 
1298.1 
1301.8 
1305.6 
1309-3 
1313-0 
13167 
1320.4 
1324.1 
1.327-8 
1331  5 
1335-2 
1338-9 
1342-6 
1346  3 
1350-0 
1353.7 
1357.4 
1361  1 
1364.8 
1368.5 
1372-2 
1375.9 
1379.6 
1383-3 
1387.0 
1390-7 
1394.4 


400 
1 

2 
8 
4 
ft 
G 
1 
8 
9 

41(1 
1 

2 
3 
4 
ft 

'  6 
7 
8 
9 

42<i 
1 

2 
3 
4 
ft 
6 
7 
8 
9 

430 
1 

2 
8 
4 
ft 
6 
7 
8 
9 

440 
1 

,2 
8 
4 
ft 
G 
7 
8 
9 

450 
1 
2 
3 
4 
ft 
G 
7 
8 
9 

460 
1 
2 
8 
4 


1396.3  1398  1 


1400-0 
1403 
1407.4 
1411.1 
1414-8 
1418.5 
1422-2 
1425.9 
1429.6 
14.33.3 
1437.0 
14407 
1444.4 
1448.1 
1451.9 
1455  6  1457.4 
1459-31461.1 

1463.0  1464,8 
14667  1468.5 
1470.4  1472.2 

1474.1  1475.9 
1477.8  1479-6 


1401.8 
1405.6 
1409.3 
1413.0 
14167 
1420  4 
1424.1 
1427-8 
1431.5 
1435.2 
1438.9 
1442.6 
1446.3 
1450.0 
1453.7 


1481-5 
1485.2 
1488.9 
1492.6 
1496.3 
1500.0 
1503  7 
1507-4 
1511 
1514.S 
1518-5 
1522  2 
1525  9 
1529  6 
1533.3 
1537.0 
15407 
1544.4 
1543.1 
1551.9 
1555  6 
1559.3 
1563.0 
1566.7 
1570.4 
1574.1 


B. 


1433  3 
1487.0 
14907 
1494  4 
1493.1 
1501-8 
1505.6 
1-509.3 
1513-0 
1516-7 
1520.4 
1524.1 
1527.8 
1.531.5 
1535.2 
1538.9 
1542.6 
1546.3 
1.550.0 
1553.7 
1-557.4 
1561.1 
1564.8 
1568-5 
1572-2 
1575.9 


1577-8  1579.6 
1581.5  1583-3 

1585.2  1587.0 
1588-9  15907 
1592-6  1594.4 

1596.3  1598-1 
1600-0  1601-8 


400  1481.5  1483.3 


9 

470 
1 

2 
8 
4 
ft 
G 
7 
8 
9 

4S0 
1 
2 


7 

8 
9 

490 


1603.7 
1607.4 
1611.1 
1614  8 


1618.5  1620.4 


1622.2 
1625-9 
1629  6 


1633.3  1635.2 


1637.0 
1610.7 
1644.4 
1643.1 
1651.9 
1655.6 
1659.3 
1663.0 
1666.7 
1670-4 
1674-1 
1677.8 
1681.5 


1685.2  1687.0 


1688.9 
1692.6 


1693.3  1698.1 


1700.0 
1703.7 
1707.4 
1711.1 
1714.8 
1718.5 


ft  1722.2  1724.1 
G 
7 


1725.9 
1729.6 
1733-3 
1737.0 
1740-7 
1744.4 
1748.1 
1751.9 
1765.6 
1759  3 
1763  0 
17667 
1770.4 
1774.1 
1777.8 
1781.5 
1785.2 
8'1788.9 
4|l792.6 

5  1796.3 

6  1800.0 
1803.7 
1807.4 
1811.1 
18148 

Iil8l8.5 

2  1822.2 

3  1825.9 
4' 1829.6 
ft'l833.3 

6  1837-0 

7  18407 


8'l844.4  1846.3 


9  1848.1 


500.1851.9  18537 


1605.6 
1609.3 
1613.0 
1616.7 


1624  1 
1627.8 
1631-5 


1638.0 
1642.6 
1646-3 
1650.0 
1663.7 
16j7.4 
1661.1 
1664.8 
1668.5 
1672.2 
1675.9 
1679.6 
1683.3 


1690 
1694.4 


1701.8 
1705.6 
1709.3 
1713.0 
1716.7 
1720.4 


1727.8 
1731.5 
1735-2 
1738.9 
1742.6 
1746-3 
1750.0 
17537 
1757.4 
1761.1 
1764.8 
1768.5 
1772  2 
1775.9 
1779.6 
1783.3 
1787.0 
17907 
1794.4 
1798.1 
1801.8 
1805.6 
1809.3 
1813.0 
1816.7 
1820.4 
1824.1 
1827.3 
1831.5 
1835.2 
1838.9 
1842.6 


1850.0 


500 
1 
2 
8 
4 
ft 
G 
7 
8 
9 

510 
1 
2 
8 
4 
ft 
G 
7 
8 
9 

520 


4 

ft 
G 
7 
8 
9 
180 
1 
2 
8 
4 
I 
G 


9 

540 
1 


Content. s, 
Cn.  Yil^. 


A. 


1851-9 
1855-6 
1859-3 
1863-0 
1866  7 
1870.4 
1874.1 
1877.8 
1.381.5 
1885, 
1888.9 
1892.6 
1896.3 
1900.0 
1903 
1907.4 
1911- 
1914-8 
1918-5 
1922.2 
1925.9 
1929-6 
1933.3 
81937  0 
1940-7 
1944-4 
1948.1 
1951-9 
1955.6 
19-39.3 
1963.0 
1963.7 
1970.4 
1974.1 
1977.8 
1981.5 
193.5.2 
19S8.9 
81992.6 
1996.3 
2000.0 
2003.7 
2007.4 
2011.1 
2014.8 
2018.5 


G  2022-2  2024.1 


7 
8 
9 

550 
1 
2 
3 
4 
ft 
G 
7 
S 
9 

560 
1 

2 
8 


8 
9 

570 
1 

2 
8 
4 
ft 
G 
7 
S 
9 

580 
1 
2 
3 
4 

r. 


8 
9 

590 
1 
2 
3 
4 
ft 


8 
9 

600 


18.53.7 
18.57-4 
1861.1 
1864.8 
1 868.5 
1872.2 
1875.9 
1879.6 
1883.3 
1887.0 
1890  7 
1894-4 
1898-1 
1901-8 
190.3-6 
1909-3 
1913-0 
1916-7 
1920-1 
1924.1 
1927-8 
1931.5 
193.5-2 
1933-9 
1942-6 
1946-3 
19-50.0 
19.537 
19.37.4 
1961.1 
1961.8 
1 968.-3 
1972.2 
1975.9 
1979-6 
1983  3 
1987-0 
19007 
1994-1 
1903-1 
2001-8 
2005.6 
2009  :i 
2013.0 
2016.7 
2020.4 


2025.9 
2029.6 
2033-3 


Contents, 
Cu.  Yds. 


2027. .3 
2031.5 
2035.2 


2037.0  2033  9 
2040.7  2042.0 
2041.4:2046.3 

2048.1  2050.0 
2051.9  2053.7 
2055.6-2057.4 
20.59.3  2061-1 
2063.0:2064  8 
2066.7  2068.5 
2070.4  2072.2 
2074.1  2075.0 


2079.6 
2083..3 


2077.8 
2081  5 

2085.2  2087.0 
4  2088  9  2090.7 

2092  6  2094.4 

2096.3  2098.1 
2100.0  2101.8 


2103.7i 

2107.4 

2111-1 

2114-8 

2118-5 

2122  2 

212.3.9 

2129-61 

21.33-3 

2137-0 

2140  7 

2144  4 

2148.1 


2105.6 
2109-3 
2113-0 
2116,7 
2120.4 
2124-1 
2127.S 
2131.5 
2135.2 
2138.0 
2142.6 
2146.3 
21.50.0 


2151-9  2153.7 
2153-6  21-37.4 


21.59.3 
2163.0 
2166  7 
2170.4 
2174.1 
2177.8 
2181.5 
218.3.2 
2188.9 


2161-1 
2161.3 
2168.5 
2172.2 
2175,0 
2170  6 
2183.3 
2187-0 
2190-7 


2192-6  2194.4 
2196.3  2198.1 
2200-0  2201  8 

2203.7  2205.0 

6  2207.4  2209.3 

7  2211  1  2213.0 

2214.8  22167 
2218.52220.4 
2222.2  2224.1 


2231.5 
2235.2 
2233.9 
2242.6 
2216.3 
2250.0 
2253  7 
22.57.4 
2261.1 
2264.8 
2268.5 
2272.2 
2275.9 
2279.6 
2283.3 
287.0 


600  2222-2' 2224  1 
l'2225.9  2227-8 
212229.6' 
312233  3 
4  2237.0 
5 '2-240.7 
G  2244.4 
7,2248.1 

8  2251.9 

9  2253.6 
6  10  22-39.3 

1  2263  0 

2  2266.7 

3  2270.4 

4  2274.1 

5  2277.8 

6  2281-5 
7;2;85  2, 

8  2238  9  2290 

9  2292-6  2294.4 
G20  2296.3  2298.1 

1  2300.0  2301.8 

2  2303712305.6 
8  2307.4  2309.3 
4  2311.lj2313.0 
ft  2314  8  2316.7 

6  2318  5  2320.4 

7  2322.2' 2324.1 

8  2325  9  2327.8 

9  2329.6 '233 1-5 
G30  2333,3  2335.2 

1  2337-0  233-<-0 

2  2340712342  6 

3  2344.4  2346.3 

4  2348-1  23-30.0 

5  2351.9  2353.7 

6  ■2335.6  2337.4 

7  2339.3  2361.1 

8  2363.0  2364.8 

9  -2306.7  2368.5 
640  2370.4  2372.2 

1  2374.1  2375.9 

2  2377-8  2379-6 

3  2331.5  2.383.3 
"4  2333.2  2337.0 

6  2388.9  2390.7 

6  2392-6  2304  4 

7  2306.3  239^.1 

8  2400.0  2401.8 

9  2403.7  2405.6 
650  2407.4  2409.3 

1  2411.1  2413.0 

2  2414-8  2416  7 

3  2418.5  2420-4 

4  2422  2  2424  1 

5  2425.9,2427  8 

6  2429-6  2431.5 

7  2133  3  2435.2 
8 '2437. 0,2438  9 
9 '24407: 24 42.6 

G6s>|-2444  4  2446.3 

1  2448  1 '24.50.0 

2  2151,9  24,537 

3  24-35.6  2457-4 

4  2459-3  2461-1 
6'2463.0  2464-8 
6'24667l2468  5 
7'2470.4'2472  2 
8'2474.1  2475-0 
9'2477.8  2479.6 

670'2181.5l24-<3.3 
l'248.5.2'2487.0 

2  •2433.9 '24907 

3  2492.6'2494.4 

4  2496.3  2498.1 

5  2500.0  2-301.8 

6  2503.7  2505.0 

7  2507.4  2509.3 

8  2511.1  2.313.0 

9  2314.8  2616.7 
680:2518.5  2520.4 

12.322.2  2524.1 

2  2325.9  25:^7.8 

3  2329  ;  2531.5 
4;233.3.3  2535.2 
ft  2537.0  2-538.0 

6  2540  7  2542  6 

7  2644.4,2546.3 

8  2.548  1  2.360.0 


9 


2351.9  2.353.7 


690 '2  335.6  2-357.4 
1  2.339.3  2561.1 
2|2563-0  2-564.8 
3  2566,7  2-368.5 
2-570,4  2372.2 
2574.1 '2.375.9 
2.377.8  2.579-6 

2581.5  2583-3 
2.585.2  2587-0 
2388.9  2690.7 

2592.6  2594.4 


4 

ft 
6 
7 
8 
9 

700 


Conents, 
Cu.  Yds. 


730  2592.6  2.594.4 
1  2506.32598-1 
2600,0;2601-8 
260371260.5-6 
•2607.4  2609.3 
•2611.lj2613.0 
-26 14.8 1 26 16.7 
2618.5  26-20,4 
2622.22624.1 
■2623.9|26'27.,H 
•26-29  6  2331.5 
2633  3  2635  2 


8 
9 

710 
1 

2 

8 


ft 
6 
7 
8 
9 

720 
] 
2 
3 


2637.0 
•26107 
4  '2644.4 
•2648-1 


2638.0 
2642.6 
'2646.3 
26.50.O 


2651  9,26.53.7 
2G55.6i26.57.4 
26.59.3  2661.1 
2663.0  2664.8 


2666.7 
2670.'* 
'2674.1 


2668.5 
'237'2.2 
2673.9 


2677.8  2679.6 


'2633.3 
2687.0 


7 

9 
40 
1 
2 
3 
4 
ft 
G 
7 
8 
9 

750 
1 

2 

8 
4 
I 
G 
7 
8 
9 

760 
1 
2 
3 
4 
5 
6 
7 


800 
1 

2 

8 
4 
ft 
6 
7 
8 
9 

810 
] 

2 
8 
4 

I 


•2701.8 
■2705.0 
707.4  2709.3 
[  2713.0 


•2724.1 

2727.8 
2731.5 
■2735.2 
273S.0 
'2742.6 
•2746.3 
2750.0 
2763.7 


4'2681.5 
ft  1 2685.2 
6  2688.9  2690 
7 '2602.6  2694.4 
Sl2696,3  '2698-1 
9  2700-0 
730-2703 
1 

2-2711.1 
3'2714.8  27167 
4  '2718.6  2720.4 
2722  2 

6  -2725-0 
'2720.6 
2733.3 
2737.0 
2740.7 

44.4 
2748.1 
2761.9 

•27.35.6|27.57.4 
2759.32761.1 
2763.0 '2764.8 
2766.712768.5 
•2770.4''2772.2 
'2774.l!2775.9 
2777.8 '2779.0 
2781.5  2783.3 
2785.2  2787.0 
2788.9, '2790.7 
792.6''2794.4 
•2796.3  2798.1 

2800.0  2301.8 

2803.7  2805.6 
2307.4  2809.3 

2811.1  2813.0 

2814.8  '28167 
'2318.6 '2820  4 

2322.2  28'24.1 
•28'25.9  2827.8 
2829  6  2831.5 

2833.3  2835.2 
2837.0  2838  9 

.  '2840  7  2842.(> 

8  -2844  4  2846.3 
9-2848.1  28.5O.0 

7  70' 235 1.9  •28.537 
l'2S-35.6  '28-37.4 

2  '23.39  3  2861.1 

3  2863.0  2864.3 

4  -2866-7  2868.5 
ft  '2870-4  2872  2 
6 '2874-1  2875-9 

7  2877-8  2879-6 

8  -2881.5  2883-3 

9  2885.2  2887.0 
780 '2888.9  2890.7 

1  2392.6  '2894.4 

2  2806.3  2898.1 

3  2900-0  2901.8 

4  2903.7  2905.6 

5  2907.4  2909 

6  2911.1  '2913  0 

7  2914.8  2916 
H '2918.5  2920.4 

9  2022.2  '2924.1 
790  '20'2.3-9  2927.8 

1  2929-6  2931-5 

2  '2933.3  2935.2 

3  2937-0  2938  9 

4  2940.7  '2942.6 

5  2944.4  2946,3 

6  2943.1  2960.0 

7  2951.9  2953,7 

8  '29.36.6  2967.4 

9  29.30,3  2961.1 
800  2963.0  2964,8 


t 

8 
9 

820 
1 
2 
3 
4 
ft 
G 
7 
8 
9 

880 
1 
2 
3 
4 
ft 
6 
7 
8 


Contents,  j  I  Contents, 
Cu.  Yds.   I  Cii.  Yds. 


A.  B. 


2963.0  2934.8 
2966,7  2968  5 

;970.4  2972.2 

2074.1  2976.9 
•2977,8  2979.6 
2931  6 '2983.3 

2985.2  2987.0 
•2988.9  2990.7 
•2992.6  2994,4 

2996.3  •2998.1 
.3000.0  3001  8 

3003.7  3005.6 
;007,4  3009.3 

3011.1  3013  0 

3014.8  3016.7 

3018.5  3020,4 
6  3022.2  3024.1 

.3025,9  3027.8 

3029.6  3031.5 

3033.3  3035.2 

3037.0  3038.9 
3J40.7  3042.3 
3044  4  3046.3 

3018.1  30-30.0 
3051-9  30.53-7 
30-35.6  30-57.4 
30.39.3  3061.1 

3063.0  3064.8 
3066  7  3068.5 

3070.4  3072.2 

3074.1  3075.9 
3077.8  3079.6 
3081.6  3083.3 

3035.2  3037.0 
30:!8.9  3090.7 
3092.63094.4 

3096.3  3098.1 
3100.0  3101.8 
31037  3105.0 


840 
1 


9  3107.4 
3111.1 
3114.S 
2  3118.5 
3122-2 
3126.9 
31'29.6 


850 
1 
2 


86 


11093 
3113.0 
31167 
3120.4 
124.1 
3127.8 
3131, 


3133  3  3135  2 


3137.0 

8  3140.7 

9  3144.4 
3148.1 
3151.9 

_  315.3.6  3167.4 
3  3159.3  3161.1 
3163.0  3164.8 
3166.7 


3174.1 


3138.0 
3142.0 
3146.3 
3160.0 
31.53.7 


3168.5 
3170.4  3172.2 


3176.0 


3177.8  3179.6 
3181.531833 


3187,0 
3190,7 


3185.2 
3188.9 

319'2.6'3194.4 

3  3196.3  3'08.1 

4  3-200.0  3201.8 
ft  3'203,7  3^206.6 

6  3^207 .4  3^209.3 

7  3211.1  3213.0 

8  3214.8  3216  7 

9  3218  5  3^2^20.4 
870  3222.2  3224.1 

1  32^25.9  3-227.8 

2  32.9.6:3231.5 

3  3233.3  3235.2 

4  3237.0 '3 238  0 
ft  3240  713242.6 
G  3244.4  3246.3 


3260.0 

3253 

3257.4 


3^248.1 

8  3251.9 

9  3^255.6 
880  3-2.5a.3  3261.1 

1  3263.0  3264.8 

2  3266,7  3^268.5 
8  3270.4  3^272,2 


8 
9 

890 
1 


4  3274.1 
6L3^277.8 
6.3'28l.5 
7  3'285.2 
3238.9 
3-292,6 
3296,3 


3300.0. 330 1..S 


2  3303.; 


8  3307.4  3309.3 


4  3311.1 


3314.8  3316. 


3318.6 
3322.2 


33-Z5.9  3327.8 


3329.6 


900  3333.3  3335.2 


3'276.0 
3279.6 
3-283.3 
3287.0 
.3200.7 
3204  4 
3-298.1 


3305.6 


.3313.0 


3320.4 
3.324.1 


900 
1 


4 

ft 
G 
7 
8 
9 

910 
1 
2 

3 
4 
ft 
G 
7 
8 
9 


3331.5 


33.3.3.3  3335  2 

3337.0  3338-9 
3340-7  3342.6 

3344.4  3346.3 

3348.1  3350.0 
3351.9  33.337 

3355.6  3357.4 
33.59.3  3361.1 

3333.0  3364.8 

3366.7  3368.5 
3370  4  3372.2 

3374.1  3375.9 

3377.8  3379.6 

8381.5  3383.3 
333.3.2  33>7.0 

3388.9  3390.7 

3392.6  3394  4 
3396.3  3398.1 
3100.0  3401.8 
34037  3405  6 

920  3407.4  3409.3 
l;3411-l  34130 

2  3414.8  .3416-7 

3  3418  6  3420.4 

4  .34-22.2  34-24.1 

6  3425.9  34-27.8 
G  3429.6  343 1 .5 

7  3433  3  3435.2 

8  3437.0  3438.9 

9  3440.7  3442.6 
98  0  3  444.4  3446.3 

1  3448.1  3450.0 

2  3451.9  34-53.7 

3  3455.6  3457.4 

4  34.59.3  3461.1 
ft  3163.0  3464-8 
G34667|3468.5 
7,3470.4,3472.2, 
8  3474.1  3475.9 
9|3477.8  3479.6 

940  3481.5'3483.3 
l'348.3.2'3 187.0 

2  3483.9  34907 

3  349'2-6'3494  4 

4  3406.3  3408.1 
5,3.300-0'3-501-8 

6  3503-713505-6 

7  ;.3507.4  3.509.3 

8  3511.1  3513.0 

9  3514.8  35167 
950'3518.5'3520.4 

l:35'22.2'3524.1 
3.5'2.5.9|3527.8 

3  3529.6  3331.5 

4  3.333.3  333.3.2 
ft  3.337.0  3.538.9 
613540.7  3.342-6 
713644.4  3.346.3 
813648.1  36,50.0 
9  3561.9  3.3537 

960  35.35.6  3,=i57.4 

1  3,5.59,3  3561  1 

2  3563.0  3,564  8 

3  3566,7  .3568.5 

4  3570.4  3.572  I 

5  3574.1  3575  9 

6  3577.8  3,579.6 

7  3.581.6  3.383.3 

8  3585.2  3587.0 

9  3.388.9  3590,7 
970  3.59-2.6  3,394.4 

1  3.396,3  3598.1 

2  3600.0  3601.8 
8  3603.7  3605,6 
4  3607.4  3609,3 
ft  3611.1  3613.0 

6  3614.8  3616,7 

7  3618.5  3620.4 

8  3622.2  3624.1 

9  36-25,9  36-27,8 
980  36'>9.6  3631,5 

1  3633,3  3635.2 

2  3637.0  3638.9 

3  3640.7  3642  6 

4  3644.4  3646  3 
ft  3648.1  3650.0 
G  3651.9  3653.7 

7  36.3-5.6  3657.4 

8  36,39.3  3661.1 

9  3663.o!3664.8 
990  3666.713668.5 

1  3670.4  3672.2 

2  3674.1  3675.9 

3  3677.8  3679,6 

4  3681.5  3683  3 
ft  3685.2'3687,0 

6  3688.9  3600.7 

7  .3692.6  3694.4 

8  3696.3  3698.1 

9  3700.0  3701.8 
100  0  3703.71 


RATIOS  OF  CORRECTION  FOR  AVERACE  END  AREA  CALCULATIONS. 


WIDTH  OF 
UUAO  liEU. 


Arpa  of 


l.'J5    2  2.5 


I  H  i^'ht  ur 
I       Sill  'it  KikI. 


Ita  io  nt 
y.nil 
Areas. 


1:1 

1:1.2 

1:1.4 

1:1. n 

1:1.8 

1:2 

1:2.5 

1::J 

i-.i.r, 

1:1 

1:1:..> 

J:') 

1  :-).■> 

l:(t 

1 :(!..-, 

1:7 

1:7.5 

1:S 

l:s.5 

l:i» 

1:;).5 

1:10 


Vurj  iii^' 
•  II  a,  1 

Si  I'K. 


.001 
.002 
.007 
.012 
.019 
.OXi 
.015 
.050 
.0(i7 
.076 
.0S5 
.09.3 
.100 
.107 
.113 
.119 
.124 
.128 
.133 
.13S 
.142 


1      1  1 


Slope. 


1:1 


1J:1 


001  001 
oo:i  .004 
001)  .007 


illO 

014 

023 

032 

041 

050 

057 

065 

07 

077 

083 

089 

094 

100 

106 

111 

117 

123 


.012 
.018 
.032 
.043 
.0i5 
.066 
.075 
.083 
.0911 
.0981 
.105 
.110 
.115| 
.120 
.1251 
.130' 
.134i 
.138' 


.001 

.004 

.008 

.01 

.022 

.033 

.044 

,056 

.06 

.076 

.084 

.092 

.100 

.106 

,111 

.116 

.122 

,127 

132 

136 

140 


2—12 


2.25    to  100 


14 


100 


Slope. 


Slope. 


16 


18 


100 


6.04  5.2  4.745,74  4.81  4.415.14  4.45  4.13  4.72  4.14  3.884.33  3.87  3.644.00  8.62  3.43 


Slope. 


001 
002 
004 
006 
009 
016 
023 
030 
.1138 
,043 
,049 
,055 
060 
(165 
070 
075 
079 
084 
088 
092 
097: 


1:1 


.001 
.004 
.006 
010 
.014 
;026 
037 
.047 
.057 
.066 
,074 
.081 
.088 
.094 
.100 
,105 
110 
115 
120 

125; 

130 


1^:1 

.001 
.004 
.007 
.011 
.015 
.027 
.040 
.051 
.061 
.070 
.078 
.084 
,093 
.099 
,105 
110 
,115 
120 
12" 
130 
135 


1:1 


1:1 


1^:1 


.001  .001  .001 

.002. (i(t;;  .003 


003  .006 


.005 1 
.006 
012 
.019 
.026 
.033 
.039 
.044 
.050 
.055 


.010 


.006 
.010 


.014  .014 
.024.026 
.035  .037 


.045 
.054 
062 
.070 
.077 

.084'.0S8 
060  .09o[  095 
,065  .095  . 101 
069'.100|.105 
073  .106  .111 


.047 

.05H 

.0(;, 

.071' 

.030 


077 

082 


111  .116 
.116  .121 
086  .121  .125 
090. 1261. 130, 


i:l 


.001 
.002 
.003 
.005 
.010 
.016 
.022 


1:1 


.001 
.003 
.006 
.010 
.014 
.024 
.033 
.042 


.029  .051 
.035!.059 
.040  .066 
.0461.073 
.051  .079 
.056  .085 
.060  .091 
.064  .09'i 


.068 
.072 
.076 
086 
.084 


.101 
106 

ml 

116 
120' 


.001 
,003 
,006 
010 
,014 
025 
,035 
047 
054 
062 
070 
078 
085 
091 
097 
102 
107 
112 
117 
121 
126' 


100 


Slope. 


,001 
,002 
,003 
005 
010 
014 
020 
025 
0311 


1:11^:1 


.001 
.003 
.006 
.009 
.013 
.022 
.031 
.039 
.048' 
055 


036' .063 
042  .070 


047 
051 
055 
058 
062 
065 
069 
072 
075 


.071 
.08-. 
.088 
.093 
.098 
.102 
.106 
111 
.116 


.001 

.003 
.006 
.009 
.013 
.021 
.034 
.014 
.052 
.000 
.068 
.075 
.082 
.0,s,s 
.093 
.098 
.103, 
.108 
,113 
,117 
122 


20 


100 


100 


24 


100 


Slope. 


hi 


001 
002 
,003 
)05 
.010 
.014 
.019 
.023' 
.028 
.033 
.037 
.041 
.045 
.049 
.053 
,056 
.060| 
.063 
.066 
.069' 


1:11^:1 

.001  .001 
.003  .003 
.005  .005 
.008  .009 
.012.013 
.020  .023 
.028  .033 
.037  .042 
.045  .050 
.053  .058 
060.066 
.066  073 
.072  .079 
.078  .085 
.083  .090 
.088  .095 
.093  .100 
.097  .104 
.102  .109 
.106  .113 
111  .118 


Slope. 


Slope. 


i:l 


1:1 


 Looi'.ool 

001!.003i.003 


002.005 
003  .007 
005|.011 
0o9i.019 
014'  026, 


.019 
.022 
,026 
,030 
034 
,037 
041 
044 
047 
050 
054 
,057 
060 
063 


.005 
.008 
.013 
.021 

.030 


.034'  0  !9 


.042 
.049 
.056 
.062 
.06S 
.074 
079 
.084 
.OS!) 
.094 
.098 
.103 
.107 


.047 
.055 
.062 
.069 
.075 
.081 
.080 
.091 
.095 
.100 
.105 
.110 
.114 


4.1 


001 
002 

ro3 

.005' 
.010 
.013 
.017  j 
0211 
()24 
.028 
.031 
.034 
037 
040 
043 
047 
050 
053 
056 
059 


1:1 

.001 
,003 
,005 
,007 
,010 
,017 
,025 
,032^ 
,039 
046 
053 
,059 
064 
070 
075 
080 
084 
088 
093 
098 
102 


1J:1 

.001 
.003 

.005 

.00, 

,012 

,020 

028 

036 

,045 

,052 

059 

,066 

,07 1' 

077 

082 

0S7 

092' 

097 

lol 

lOi 


26 


28 


100 


100 


30 


100 


3.71  3.43  3.24I3.47  3.20  3.07  3.24  3.20  2.91 


Slope. 


001 
.002 
,003 
005 
,008 
,012 
016 
019 
022 
025 
028 
031 
034 
037 
010 
043 
046 
048 
051 


i-A  1:1 

.001 
.002 
.004 
.006 
009 
016 
.023 
.030 
037 
,044 
.050 
.055 
.060 
065 
.070 
075 
080 
084 
.088 
.093 
054  .097 


.001 

.003 

O05 

.008 

.011 

019 

.02' 

.034 

,042 

,050 

,057 

063 

069 

075 

080: 

085^ 

089 

094 

098 

102 

107 


Slope. 


i:l  1:1  15:1 


.001  .001 
.002  .002 
.001  .005 
.006  .007 
.009  .010 
.015  .018 
.022  .025 
.029  .033 
.03k.040 
.04r.018 
.018  .054 
.053  .060 


001 
001 
.002 
003 
.006 
010 
013 
016 
019 
022 
025 
027 
030 
033 
036 
OSS 
041 
044 
046 
049 


.058 
.063 
067 


.066 
072 
.077 


.072L082 
.076'. 086 
.080.091 
.084  .095 
.088  ,100 
.092  .104 


Slope. 


i-A 


.001 
.001 
.002 
.')03 
.005 
.008 
.011 
.014 
.016 
.019 
.021 


I 

1:1  l',:l 


001  .001 

002  .002 
.004  .005 
006  .00 
.008.010 
014'.017 
021 '.024 
027  .032 
034  .039 
.040  .046 
045  .052 
.050  .0-58 

024  .0.55  .064, 
.026  .060  .0(!9 
029  .064  .074 
031  .068  079 
.034  .072  .084 
.036  .076  .088 
.039  .079  .092 
041  .083  .096 
044  .087  .100 


liiitio  of 

ElMl 

Arras. 


1:1 
1:1.2 
1:1.4 
1.6 
1.8 


1: 
I: 
1:2 
1:2.5 
I::l 
1:3.5 
1:4 
1.4.5 
1:5  I 
1:5.5 
1:6 
1:6.5 
1:7 
1:7.5 
1:8 

1:!) 
I:!).5 


On  Estimating  Earthwork. 

The  accompanying  table  is  designed  to 
facilitate  the  computation  of  earthwork 
after  the  areas  of  the  cross  sections  have 
been  obtained.  The  areas  may  be  ob- 
tained by  calculation  from  the  field  notes  ; 
or  the  cross  sections  may  be  plotted  and 
the  areas  obtained  by  the  planimeter. 
I'he  former  method  is  short  and  easy  in 
a  level  country,  but  where  the  surface  of 
the  ground  is  broken  and  irregular  the 
latter  method  is  to  be  preferred.  Plotting 
the  cross  s  ections  also  makes  a  complete 
record  of  the  work,  with  its  classification 
at  every  point,  and  allows  revision  and 
deviation  within  the  limits  to  which  the 
section  is  taken,  by  siiii[)ly  indicating  the 
position  of  the  centre  line.  Usua'ly  it 
will  be  found  easiest  to  plot  the  rods 
from  a  line  assumed  as  the  height  of  in- 
strument ;  but  when  the  work  is  extend- 
ed so  as  to  involve  several  heights  of 
itistrument  in  the  same  section,  or  when 
the  work  is  to  be  used  for  a  great  Lumber 
of  calculations  fir  successive  estimates, 
it  will  be  found  cheapest  to  work  from 
elevations. 

A  c>nvtnient  form  for  the  estimate 
sheets  is  here  shown.  In  the  two  first 
columns  are  entered  the  stations  and 
ploj>es  at  which  the  cross  sections  are 
taken.  The  column  headed  ''Length  in 
Feet "  is  filled  up  by  subtracting  the 
numbers  in  these  two  first  columns.  The 
columns  headed  "  Area  uf  Gross  iSedion  " 
are  filitil  up  with  areas  obtained  either 
from  calculation  or  I'rom  measurement 
by  the  planimeter.  In  the  columns  head- 
e<i  "^ycraf/e  ^mt "  are  entered  one-half 
the  sums  of  the  areas  of  adjacent  cross 
sections.  If  preferred  the  sums,  in.-tead 
of  the  half  sums,  may  be  used,  in  which 
case  the  final  conttnts  will  be  doubled. 

The  main  columns  of  "  Contenls  in 
Cubic  Y(ird-i^'  are  now  filled  up  by  aid 
of  accompanying  "  Tuble  of  Cubic  Yurds 
in  Lengths  of  lUO  Feet."  If  the  lengths 
are  I'lQ  feet  the  corresponding  quantities 
are  simply  transferred  fiom  the  table.  If 
the  distance  is  50  feet,  one  half  the  quan- 
tity is  transferred.  If  the  distance  is  25 
feet,  one-fourth,  &c.  Usually  the  opera- 
tion can  be  performed  mentally.  The 
table  being  set  up  before  one,  the  arrange- 
ment of  it  is  such  that  the  eye  knows  just 
where  to  strike  for  a  quantity.  There 
are  no  leaves  to  turn.  (Quantities  can  be 
entered  as  fast  as  one  can  write.  Blue 
ink  may  be  u.sed  in  writing  quantities  in 
excavati'>n,  and  red  ink  in  writing  quan- 
tities in  embankment. 

The  calculation  of  earthwork  by  the 
method  of  averaging  end  areas  is  not 
theoretically  correct,  excepting  in  the 
two  special  cases :   one  when  the  end 


areas  are  equal,  and  the  other  when  the 
prismold  has  two  of  its  longitudinal 
bounding  planes  parallel.  As  that  por- 
tion of  every  roadway  prisraoid,  which 
lies  between  the  vertical  planes  passing 
through  the  edges  of  the  roadbed  is 
practically  included  in  the  latter  condi- 
tion, it  follows  that  the  variation  from 
the  true  contents,  obtained  from  averag- 
ing end  areas,  lies  outside  the  central 
roadbed  prism,  and  we  may  consider  it  as 
dependent  on  the  four  following  factors : 

1st.  The  ratio  of  the  end  areas  of  the 
prismoid. 

2nd.    The  width  of  the  roadbed. 
3rd.    The  degree  of  the  slope. 
4th.    The  heighth  of  the  section. 

This  variation  has  been  investigated 
with  the  result  shown  in  the  table  called 
"  Mutios  of  Correction  for  Average  End 
Area  Calculations."  The  manner  of  pro- 
ceeding was  briefly  thus :  With  the  data 
shown  in  the  heads  of  the  columns  in 
the  table,  and  in  the  left  hand  column, 
the  true  contents  of  the  prisms  by  the 
prisrnoidal  formula  were  found,  as  well 
as  the  contents,  by  averaging  end  areas. 
The  ratio  of  variation  in  many  par- 
ticular cases  being  thus  found,  the  curve 
of  variation  for  each  class  was  formed 
by  measuring  the  ratios  of  end  areas 
on  the  axis  of  abscissas,  and  the  per- 
centages of  variation  on  the  axis  of  ordin- 
ates.  Some  maxima  and  minima  of  these 
curves  were  also  traced,  which  seemed 
to  differ,  in  extreme  cases,  10  per  cent,  or 
so  from  the  mean  given  in  the  table.  It 
is  believed  these  deviations  will  usually 
counterbalance  one  another.  If  the  work 
is  of  a  peculiar  nature,  so  the  general 
cases  here  worked  out  will  not  apply,  cor- 
rections applying  to  it  can  be  worked  out 
and  entered  in  one  of  the  blank  columns. 

To  apply  the  table  of  corrections,  we 
divide  one  area  of  cross  section  by  its 
neighbor,  and  take  from  the  table  its  cor- 
responding ratio  or  percentage  of  correc- 
tion and  multiply  the  contents  by  it, 
writing  the  result  in  the  column  headed 
"  Correction."  The  special  case,  when 
one  end  is  zero,  or  ends  at  grade,  is  not 
provided  for  in  table  of  correcticms.  For 
this  case  the  correction  is,  the  slope  area 
multiplied  by  one  sixth  the  length.  For 
the  road  bed  area  being  the  base  of  a 
wedge,  the  solidity  is  one-half  base  nuilti- 
plied  byaltitude;  but  the  slope  areas  being 
bases  of  pyramids,  the  solidity  is  one-third 
base  multiplied  by  altitude.  One  half 
which  is  used,  less  one-third,  which 
should  be  used,  equals  the  correction,  one- 
sixth.  This  correction,  as  well  as  all 
others,  is  to  be  deducted  from  contents  in 
main  column. 


Estimited  Quantities  in  Grading. 


STA- 
TIOSS 


No. 


AUEA  OF  (  KOSS 

^KC•  ION 
IN  S({U  XUK  IT. 


Cxciiv.itioii. 


117 
118 


119 


506382635: 
85;417|297 


120 


121 


125 
123 


50  Cut  coi  nen  ces 

....I  18  16 

50158  53105. 
....630163325 


....110243485 


cnt 


ends 


31 
80103 
....'334280 

35700  277  555 
50743157 


50870156  209 
187  255 


3147 


..'821 

30534 

611  m 

70 
84 

90  mt  COM  men  ces 


ends 


CitcoiBineii  ces  68 


560 
555 
314 


AVEHAOE  AREA. 


Excavation. 


394 

 634 

 527.5 

,'263 
55 


105 

72 
218j 
517 
52  U 
,806  i 
845J 
6774 
267 


34 
108 
212 
280 
270 
121. 


170 
2784 
217 
156.1 


17  U  2.32 


130 
36^ 


15 
67^ 
2154 
426 
560J 
540 
242^ 


280 
557 1 
434,! 
261^ 


201 

m 


Em- 

b:ink 
nifnt 


Corrected  Totals, 


CONTKNTS  IN  CUBIC  YARDS. 


Escavniion. 


16.7  1 
162.916 
729.632 
1174.1 
683.8 
136  3 
40. 


11.4 
63.3 
161.9 
670.2 
400  8 
2987.0 
1565, 
752.8 
306.518 


9853.7  98 


14  8 
63.9 
200.6 
394  4 
362.9 
150  0 
90.0 


1037 
361.0 
120  6 
579  6 
317.6 
144.4 
41.9 


2945.423 


9755.7|....  2922.4;....  5278.1  ....j  82.7..., 


1/1  :s 


27.8 
125.0 
399.1 
788.9 
626.5 
300.0 
179.6 


207.4 
722.7 
241.3 
968.5 
429  6 
223.3 
84.4 


5324.1 


Em- 
liank- 
mint. 


25.1 
25.1 


7.6 

23.8 
5.1 


461  86.' 


REMARKS. 


The  error  from  calculation  by  averag- 
ing end  areas  is  not  so  great  as  appears 
at  first  sight,  or  as  it  is  often  represented. 
Taking  isolated  cases,  where  the  ratio  of 
end  areas  is  great,  it  may  be  made  to 
appear  that  the  error  is  10  or  15  per  cent.; 
but  taking  extendeil  work  the  whole 
error  is  trifling,  the  great  bulk  of  con- 
secutive cross  sections  being  nearly  equal 
to  each  other,  and  the  errors  are  distri- 
buted. The  writer  tested  one  section  of 
28,(;0  •  cu.  yds.  and  f  lund  the  error  less 
than  one  tiiird  of  one  per  cent.  What 
appeared  to  be  a  section  which  would 
show  great  error  on  account  of  crossing 
several  short  ravines  and  gullies,  con- 
taining some  85.000  cu.  yds.,  whs  less  than 
one-half  of  one  per  cent,  out  of  the  way. 

In  earthwork  there  are  only  two  sides 
of  the  prismoid  perfect  planes,  and  these 
two  are  the  theoretical  planes  of  the 
cross  section.  The  surface  of  the  ground 
is  never  a  perfect  plane.  The  rod,  in 
taking  points  usually  sinks  a  little  in  the 
ground,  the  slopes  are  not  trimmed  exact- 
ly, nor  the  grade  made  perfict.  If  there 
is  any  difference  between  the  true  so'i  lity 
and  that  obtained  by  the  method  here 
presented,  it  is  the  conviction  uf  the 
writer  that  it  would  be  easier  and  cheap- 
er for  the  engineer  to  shovel  it  than  to 
calculate  it. 

The  method  of  calculation  for  earth- 
work should  be  direct  and  simple,  so  it 
can  be  used  «afely  by  assistants  not  speci- 


ally skilled  in  intricate  calculations.  It 
is  better  for  the  engineer  to  spend  much 
of  his  time  in  the  field,  minutely  observ- 
ing and  closely  measuring  the  work,  than 
to  spend  it  ]nainly  in  the  office,  basing 
refined  coi;iput,iitions  on  erroneous  or 
careless  measurements.  The  errors  in 
measurement  will  usually  be  greater  than 
the  errors  of  c.'ilculation,  by  averaging 
end  area.s  without  correction. 


— Piililislied  bv— 

JOHN  WILEY  &  SONS, 
^cieiitifioIPul>lislierss 


15  Astor  Place. 


NEW  YORK  CITY. 


The  New  and  Complete  Catalogue 

OF  THE  PUBMCATIOKS  Or 

JOHJV  WIL.EY  &  SOIVS, 

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cop-  3 


TABLE  OF  CUBIC  YARDS  IN  LENGTHS  OF  100  FEET. 

ADAPTED  ESPECIALLY  TO  THE  CALCULATION  OF  EARTH  WORK  BY  THE  METHOD  OF  AVERAGING  END  AREAS. 


Contents  of  Column  "A"  are  for  the  integers  in  column  headed  "Area,  Square  Feet." 
Contents  of  Column  "  B  "  are  for  the  same  integers  plus  0.5  square  foot. 


COPYRJQHT  1885  BY  S.  B.  FISHER. 


Contents  for  lengths  greater  or  less  than  100  are  obtained  by  simple  proportion,  thus  :  125 
sq.  ft.  for  length  of  20  ft.=j7j=^  of  463.0  cu.  yd.s;  the  contents  for  125  sq.  ft.=92.6  cu.  yds. 


Cont'-nts, 
Cu.  Yds. 


1 

■2 
3 
4 
5 
6 
7 
f> 
9 

10 
1 
2 
3 
4 
5 
6 
7 
8 
» 

20 
1 
2 
3 
4 
5 
6 


9 
30 
1 
2 
3 
4 
5 
6 
7 
8 
9 
40 
1 
2 
3 
4 
5 
6 
7 
8 
9 
50 
J 
2 
3 
4 
5 
C 
7 
8 
9 
CO 
1 
2 
3 
4 
5 
6 
7 
8 
9 
70 
1 
2 
H 
4 
5 
6 
7 
8 
9 
80 
1 
2 
3 
4 

6 
7 
8 
9 
90 
1 
2 
3 
4 
o 
6 
7 

loci 


3.7 
7.4 
11.1 
14.8 

18.5 
22.2 
25.9 
29.« 
33.3 
37.0 
407 
44.4 
48.1 
51.9 
55.6 
59.3 
63.0 
66.7 
70.4 
74.1 
77.8 
81.5 
85.2 
8S.9 
92  6 
96.3 
lOOO 
103. 
107.4 
111.1 
114.8 
118.5 
122.2 
125.9 
129.6 
133.3 
137.0 
140.7 
144.4 
143  1 
151.9 
155.6 
159.3 
163.0 
103.7 
170.4 
174.1 
177.8 
131.5 
135.2 
138.9 
192  6 
193.3 
200.0 
203.7 
237.4 
2!1.1 
214.8 
218.5 
222  2 
225.9 
229.6 
233.3 
237.0 
210  7 
244.4 
248.1 
251.9 
2-)5.6 
259  3 
2330 
266  7 
270.4 
274 
277.8 
231.5 
235.2 
288.9 
292  6 
296  3 
300.0 
303.7 
3(t7.4 
311  ] 
314.8 
318.5 
322.2 
325.9 
329  6 
333.3 
337.0 
310 
344.4 
3181 
351.9 
3)5.6 
359.3 
363.0 
366.7 
370.4 


B. 


1.8 
6.6 
9.3 

13,0 
16,7 
20.1 
24,1 
27.8 
31.5 
35.2 
38.9 
42.6 
46.3 
50.0 
53.7 
57.4 
61.1 
618 
68.5 
72  2 
75.9 
79.() 
83.3 
87.0 
90 
944 
98.1 
101  8 
105.6 
109.3 
113.0 
116 
120.4 
124.1 
127.8 
131.5 
135.2 
1339 
142.6 
143.3 
150.0 
153.7 
157.4 
101.1 
101.8 
103.5 
172.2 
175.9 
179.6 
183  3 
187.0 
190 
191.4 
193.1 
201.8 
205.0 
209.3 
213.0 
216.7 
220.4 
224.1 
227.8 
231.5 
235.2 
238.9 
242.6 
246.3 
250.0 
253.7 
257.4 
231,1 
264.8 
263.5 
272.2 
275.V) 
279,6 
283.3 
237.0 
290.7 
291.4 
298,1 
301.8 
305.6 
309.3 
313.0 
316.7 
320.4 
324  1 
327.8 
331.5 
335.2 
338.9 
342.6 
346.3 
350.0 
353.7 
357,4 
361.1 
364.8 
368.5 
372.2 


] 

2 
3 
4 
5 
6 
7 
8 
9 

110 
1 

2 
3 
4 
5 
6 
7 
8 
9 

120 
1 

2 
3 
4 
6 
G 
7 
8 
9 

130 
1 
2 
3 
4 
h 
6 
7 
8 
9 
140 
1 
2 
3 
4 
5 
6 
7 
8 
9 

150 
1 

2 
3 
4 
5 
6 
7 
8 
9 


Contents, 
Cn.  Yds. 


A.  B. 


100  370.4 


160 
] 

2 
3 
4 
5 
G 
7 
8 
9 

17.. 
1 

t 
3 
4 
5 
0 
7 
8 
9 

180 
) 
2 
3 
4 
5 
6 
7 
8 
9 
190 
1 

a 

3 
4 
5 
6 
7 
8 
9 

200 


374.1 
377.8 
381.5 
385  2 
388.9 
39i.6 
396  3 
4000 
403.7 
407.4 
411.1 
414.8 
418  5 
422  2 
425.9 
429,6 
433  3 
437.0 
440  7 
414.4 
448  1 
451.9 
455,6 
4-59  3 
463.0 
466  7 
470.4 
474.1 
477.8 
481.5 
485.2 
488,9 
4926 
436.3 
500.0 
503.7 
507.4 
511.1 
514.8 
518.5 
522.2 
525.9 
529.6 
533.3 
537  0 
540.7 
544.4 
543.1 
551.9 
555.0 
559  3 
503.0 
566  7 
570.4 
574.1 
577.8 
531.5 
585.2 
538.9 
592  6 
596  3 
600.0 
603  7 
607.4 
611.1 
614.8 
618.5 
622.2 
625  9 
629.6 
633.3 
637.0 
640  7 
644  4 
048  1 
651  9 
655  6 
659.3 
663  0 
666.7 
670.4 
674  1 
077.8 
681  5 
6852 
688.9 
692.6 
096.3 
700.0 
703.7 
707.4 
711.1  I 
714.8 
718.5  i 
722  2 
725.9 
729  6 
733  3 
737.0 
740.7 


372.2 
375.9 
379.6 
383.3 
387.0 
.390.7 
394.4 
39.S.1 
401.8 
405.6 
409.3 
413.0 
416.7 
420.4 
421.1 
427.8 
431.5 
435.2 
438  9 
442.6 
416.3 
450.0 
453.7 
457.4 
461.1 
464.8 
468,5 
472.2 
475.9 
479.6 
4833 
487.0 
490  7 
494.4 
493.1 
501.8 
505.6 
509.3 
513.0 
510.7 
520.4 
521.1 
527.8 
531.5 
535.2 
533.9 
542.6 
546.3 
550.0 
553.7 
557.4 
531.1 
564.8 
563  5 
572  2 
575.9 
579.6 
583,3 
587.0 
590.7 
594  4 
598.1 
601  8 
605  6 
609.3 
613.0 
616.7 
620.4 
624  1 
627.8 
631.5 
635.2 
638.9 
642.6 
646.3 
650.0  ■ 
653..  , 
657.4 
061  1 
664.8 
638.5 
672  2 
675.9 
679.6 
683.3 
687.0 
690.7 
694.4 
698.1 
701.8 
705.6 
709.3 
713.0 
716.7 
'^20.4 
724.1 
727.8 
731.5 
735.2 
738.91 


Conteiiis, 

Cu.  Yd^. 

A. 

B. 

200 

740 ' 

749  f! 

1 

74,4  4 

746  2 

2 

1 

/  TO,  1 

7=in  t\ 

3 

751.E 

753  7 

4 

755  (. 

5 

759  ' 

7fil  1 

/  O  1 .  1 

e 

733  t 

ICl  S 
/  ut,o 

7 

766  7 

768.5 

8 

772  2 

9 

774. 1 

775.9 

2H' 

777.8 

779,6 

1 

781.5 

783.3 

2 

735.2 

787  0 

3 

738.1 

790.7 

4 

792.0 

794.4 

5 

796. t 

798.1 

C 

80r.( 

801.8 

7 

803.7 

805.6 

8 

807.4 

809.3 

9 

811.1 

813,0 

220 

814.8 

816.7 

1 

818.5 

820.4 

2 

822.2 

824  1 

3 

825.9 

827.8 

4 

829.6 

831.5 

ft 

833.3 

835.2 

G 

837.0 

838.9 

7 

840.7 

842^0 

8 

8444 

843  3 

9 

843.1 

850.0 

230 

85 1 .9 

853.7 

1 

855.6 

857.4 

2 

859.3 

861.1 

8 

863.0 

861^8 

4 

833.7 

863  5 

5 

870  4 

872  2 

G 

874.1 

875,9 

7 

877.8 

879^6 

8 

881.5 

883.3 

9 

835.2 

887^0 

240 

883  9 

890.7 

1 

892.3 

891.4 

2 

893.3 

893.1 

3 

900  0 

901.8 

4 

903.7 

9(i5!o 

5 

907.4 

909  3 

6 

911.1 

913^0 

7 

914.8 

916  7 

8 

918.5 

920.4 

9 

922,2 

924.1 

2.50 

925  9 

927.8 

1 

929.6 

931.5 

2 

9333 

935  2 

3 

937.0 

933.9 

4 

940.7 

942.6 

5 

914.1 

946.3 

G 

918.1 

950.0 

7 

951.9 

953.7 

8 

955  6 

957,4 

9 

959.3 

961.1 

260 

933.0 

964  8 

1 

936  7 

938.5 

2 

970  4 

972.2 

3 

974.1 

975.9 

4 

977.8 

979.6 

5 

931.5 

983.3 

6 

985,2 

987.0 

7 

938.9 

990.7 

8 

992.6 

994.4 

9 

996.3 

998  1 

300 
1 
2 
3 
4 
6 
fi 
7 
8 
9 

310 
I 

2 


C'oiit.'iiis, 
Cu.  Yds. 


27iHooo.o  1001.8 

1  1003.7  1005.6 

2  1007  4  1009.3 

3  1011.1  1013.0 

4  1014.8  1016.7 
6  1018.5  1020.4 

6  1022.2  1024.1 

7  1025.9  1027.8 

8  1029.6  1031.5 

9  1033.3  1035.2 
280  l(i37.0  1038.9 

1  1040.7  1042.3 

2  1044.4  1046  3 

3  1048,1  10.50.0 

4  1051.9  1053.7 
6  1055.6  1057.4 

6  1059  3  1061.1 

7  1063.0  1064.8 

8  1066  7  1068.5 

9  1070.4  1072.21 


29,»  1074.1 
1,1077.8 


2  1081-51083.3 
3,1085.2  1087.0 
4  1088.91090.7 


5  1092.6 
G!  1096.3 
711100.0 
8  1103.7 
1107.4 


742,6|3eo|llll.l 


1075.9 
1079.6 


4 

5 
(; 
7 
8 
9 

320 
1 
2 
3 
4 
6 
G 
7 
8 
9 

330 
1 
2 
3 
4 
5 
G 
7 
8 
9 

340 
I 

2 


5 
G 
7 
8 
9 

350 
J 
2 
3 
4 
5 
6 
7 
8 
9 

360 
1 
2 
3 
4 
5 
G 
7 
8 
9 

S70 
1 
2 
3 
4 


1094.4 
1098.1 
1101.8 
1105.6 
1109.3 
1113.0 


6 
7 
8 
9 

380 
1 
2 
3 
4 
5 
G 
7 
8 
9 

390 
1 

2 
3 

t 


1111,1 
1114.8 
1118.5 
1122.2 
1125.9 
1129.6 
1133.3 
11370 
1140.7 
1144.4 
1148  1 
I15I.9 
1155  6 
1159  3 
1163.0 
1166.7 
1170.4 
1174.1 
1177.8 
1181.5 
1185.2 
1188  9 
1192.6 
1196.3 
1200  0 
1203.7 
1207.4 
1211.1 
1214,8 
1218  5 
1222.2 
1225  9 
1229.6 
1233.3 
1237.0 
1240.7 
1244.4 
1248  1 
1251.9 
1255.6 
1259.3 
1233.0 
1206.7 
3  1270.4 
4' 1274.1 
1277.8 
1231.5 
1285.2 
1283.9 
1-92.6 
1296.3 
1300.0 
1303. 
1307.4 
1311.1 
1314.8 
1318.5 
13222 
1325.9 
1329.6 
13333 
1337.0 
1340.7 
1344.4 
1348.1 
1351.9 
1355.6 
1,359.3 
1363.0 
1366.7 
1370.4 
1374.1 
1377.8 
1381.5 
1385.2 
1388.9 
1392.6 


1396.3  1398  1 


1400.0 
1403, 
1407.4 
1.411.1 


1414.8  1416.7 


1418.5 
1422.2 
1425.9 
1429.6 
1433.3 
1437.0 
1440.7 
1444,4 
1448.1 


111.3.0 
1 1167 
1120.4 
1124.1 
1127  8 
1131,5 
1135.2 
1138.9 
1142,  1 
1146,3 
1150.0 
1 153  7 
1157.4 
1161.1 
1164.8 
1168.5 
1172.2 
1175  9 
1179.6 
1183  3 
1187,0 
1190.7 
11944 
1198.1 
1201.8 
1205.0 
1209.3 
1213.0 
1216.7 
1 220.4 
1224.1 
1227.8 
1231.5 
1235,2 
1238.9 
1242.6 
1216.3 
1250  0 
1253.7 
1257.4 
1261.1 
1234  8 
i  26S.."i 
1272,;: 
1275.9 
1279  6 
1233.3 
1287.0 
1290.7 
1294.4 
1298.1 
1301.8 
1305.6 
1309.3 
1313.0 
1316.7 
1320.4 
1324.1 
1327.8 
13315 
1335.2 
1338.9 
1342.6 
1346  3 
1350.0 
1353.7 
1357.4 
1361  1 
1364.8 
1368.5 
1372.2 
1375.9 
1379.0 
1383.3 
1387.0 
1390.7 
1394.4 


400 
1 

2 
3 
4 
6 
G 
7 
8 
9 

410 
1 

2 
3 
4 
5 

^  6 
7 
8 
9 

42ii 
1 

2 
3 
4 

5 
6 


I  ontents, 
Cu.  Yd«. 


A.  B. 


9 
430 
1 

2 
3 
4 
6 
G 


1401.8 
1405.6 
1409.3 
1413.0 


8 
9 
440 
1 
,2 
3 
4 
5 
6 
7 
8 
9 

450 
1 
2 
3 
4 
5 
6 
7 
8 
9 

460 
1 
2 
3 
4 
5 
G 
7 


1481.5 
1485.2 
1488.9 
1492.6 
1493.3 
1500.0 
1503 
1507.4 
1511  1 
1514.8 
1518.5 
1522  2 
1525  9 
1529  6 
1533.3 
1537.0 
1540.7 
1544.4 
1543,1 
1551.9 
1555  6 
1559.3 
1563.0 
1566.7 
1570.4 
1574.1 
1577.8 
1531.5 
1585.2 
1588,9 
1592.6 


1433  3 
1487.0 
1490.7 
1494  4 
1493.1 
1501.8 
1505.6 
1.509.3 
1513.0 
1516.7 
1 520.4 
1524.1 
1527.8 
1.531.5 
1535,2 
1.538.9 
1542.6 
1546.3 
1550.0 
1553.7 
1.557.4 
1561.1 
1564.8 
1.568.5 
1572.2 
1.575.9 
1579.6 
1583.3 
1587.0 
1590.7 
1594.4 


9 

470 
1 
2 
3 
4 
5 
G 
7 
8 
9 

4S0 


1600.0 
1603.7 
1607.4 
1611.1 
16148 
1618.5 
1622.2 
1625.9 
1629  6 
1633.3 
1637.0 
1010.7 
1644.4 
1048.1 
1651.9 
16.55.6 
1659,3 
1663.0 
1666.7 
1670.4 
1674.1 
1677.8 
1681.5 


1596.3  1598.1 


1601.8 
1605.6 
1609.3 
1613.0 
1616.7 
1620.4 
1624  1 
1627.8 
1631.5 
1635.2 
1638.9 
1042,6 
1646.3 
1650.0 
1653.7 
1657.4 
1661.1 
1664.8 
1668,5 
1672.2 
1675.9 
1679.6 
1683,3 


1685.2  1687,0 
1688.9  1690.7 
1692.6  1694,4 

1696.3  1698.1 
1700.0  1701.8 


1703.7 


1707.4  1709.3 


1420  4 
1424.1 
1427.8 
1431.5 
1435.2 
1438.9 
1442.6 
1446.3 
14.50.0 


1451.9  14.53.7 
1455  6  1457.4 
1459.3  1461.1 
1463.0  1464,8 


1466.7  1468.5 
1470.4  1472.2 
1474,1  1475.9 
.,  1477.8  1479,6 
400  1481.5  1483.3 


1711.1 
1714.8 
1718.5 
1722.2 
1725.9 
1729.6 
1733.3 
1737.0 
1740.7 
1744.4 
1748.1 
1751.9 
175.5.6 
17593 
17630 
1766.7 
1770.4 
1774.1 
1777.8 
1 11781.5 
2!l785.2 


1705.6 


3,1788.9  1790.7 


1792,6 
1796.3 
1800.0 
1803.7 
1807.4 
1811.1 
18148 
1818.5 
1822.2 

3  1825.9 

4  1829.6 
5,1833.3 
6:1837.0 

7  1840.7 

8  1844.4 

9  1848.1 
500.1851.9 


4 

5 
G 
7 
8 
9 
490 
1 
2 


1713.0 
1716.7 
1720.4 
1724.1 
1727.8 
1731.5 
1735-2 
1738.9 
1742.6 
1746.3 
1750.0 
1753.7 
1757.4 
1761.1 
1764.8 
1768.5 
1772  2 
1775.9 
1779.6 
1783.3 
1787.0 


1794.4 
98.1 
1801.8 
18056 
1809.3 
1813.0 
1816.7 
1820.4 
1824.1 
1827.3 
1831.5 
1835.2 
1838.9 
1842.6 
1846.3 
18.50.0 
1853.7 


9^. 


500 
1 

2 
3 
4 

5 
6 
7 

8 
9 

510 
1 
2 
3 
4 
6 
6 
7 
8 
9 

520 
1 
2 
3 
4 
5 
6 
7 
8 
9 


Contents, 
Cu.  Y.N. 


A.  B. 


1851.9 
1855.6 
1859.3 
1863.0 
1866 
1870.4 
1874.1 
1877.8 
1381.5 
1885.2 
1888.9 
1892.6 
1896.3 
1900.0 
1903.7 
1907.4 
1911.1 
1914.8 
1918.5 
1922.2 
1925.9 
1929.6 
1933.3 
1937  0 
1910.7 
1944.4 
1948.1 
1951.9 
1955.6 
1959.3 
030  1963.0 
1963.7 
1970.4i 
1974.1 
1977.8 
1981.5 
1985.2 


8 
9 
540 
1 
2 
3 
4 
5 


18.53.7 
18.57.4 
1861.1 
1864.,S 
1 868.5 
1872 
1875.9 
1879.3 
1883.3 
1887.0 
1890  7 
1894.4 
1898.1 
1901.8 
190.5.0 
1909.3 
1913.0 
1916.7 
1920.1 
1924,1 
1927.8 
1931.5 
19.35,2 
1938,9 
1942.3 
1946.3 
19.50,0 
1953,7 
1957.4 
1961.1 
1961..S 
196,S..-. 
1972,2 
1975,9 
1979.6 
1983  3 
1987,0 


1988.9  1990.7 
1992,6  1994.1 


1996.3 


2000.0  2001.8 


6  2022.2  2021.1 


7 
8 
9 
550 
1 
2 

3 
4 
h 
6 
7 
S 


2003 

2007.4 

2011.1 

2014.8 

2018.5 


9 

560 
1 

2 
3 
4 

6 


7 

8 
9 

570 
1 

2 
3 
4 
5 
6 
7 
8 
9 

580 
1 
2 


2025.9 
2029.6 
2033.3 
2037.0 
2040.7 
2041.4 
2048, 1 
2051.9 
20.55.6 
2059.3 


1998.1 


Contents, 
Cm.  Yds. 


A. 


B. 


600  2222.2  2224  1 
1 '2225.9  2227.8 

2  2229,6  2231.5 

3  2233,3  223,5.2 

4  2237.0  2233.9 
2212.6 
2216.3 
2250.0 
2253  7 


5  2240.7 

6  2244.4 

7  2248.1 

8  2251.9 

9  2255.6 
6  1  0,22.59.3 

1  2263  0 

2  2266.7 

3  2270.4 

4  2274.1 
6  2277.8 

6  2281.5 

7  2-;85  2 


22.57.4 
2261.1 
2264.S 
2268.5 
2272.2 
2275.9 
2279.6 
2283.3 
2287.0 


Conienls, 
Cu.  Yds. 


B. 


7  . :)0  2592.6  2594.4 
1 

9 


2005.6 
2009  :!  5 
2013.0 
2016.7 
2020.4 


2066.7 


2027.8 

2031.5 

2035.2 

2033  9 

2042.3 

i046.,! 

2050.0 

2053. 

2057.4 

2061  1 


2063.0  20618 


2068.5 


2070.4  2072.2 

2074.1  2075.9 
2077.82079.6 
2081  512083.3 

2085.2  -2087.0 
2038  9  2090.7 
2092  6  2094.4 

6  2096.3  2098.1 
100.0  2101.8 


G 

4 

8 
9 

590 
1 

2 
3 
4 
h 
G 


2103.7 
2107.4 
2111.1 
2114.8 
2118.5 
21222 
212.5.9, 
2129.6' 
2133.3 
2137.0 
2140.7 
2144  4 


2105.0 
2109.3 
2113.0 
2116.7 
2120.4 
2124.1 
2127.,3 
2131.5 
2135.2 
21389 
2142.3 

2146.;; 


148.1  21.50.0 
2151.9  2153.7 
2155.6  2157.4 


2159.3 


2163.0  2161. 


2166 
2170.4 
2174. 
2177.8 
2181.5 
18.5.2 


2161. 


2168 

2172 

2175 

2179  3 

2183.3 

21.37.0 


8  2238  9  2290.7 

9  2292.6  2294.4 
620  2296,3  2298.1 

1  2300.0  2301.8 

2  2.303.7  2305.6 

3  2307.4  2309.3 

4  2311.1  2313.0 

5  2314  8  2316.7 

6  2318  5  2320.4 

7  2322.2  2324.1 

8  2325  9  2327.8 

9  2329.6 '233 1.5 
630  2333.3  2335.2 

1  2337.0  233-1.9 

2  2340.7,2342  6 

3  2344.4  2343.3 

4  2318.1  23.50.0 

5  2351.9  2353.7 

6  -2355,6  2357.4 

7  2359,3  2361.1 

8  2333.0  2364.8 

9  2336.7  2368.5 
640  2370.4  2372.2 

1  2374.1  237.5.9 

2  2377.8  2379.0 

3  2331.5  2383  3 
'"4  2385.2  2387.0 

6  2388.9  2390.7 

6  2392.6  2394  4 

7  2396.3  2393.1 

8  2400.0  2401.8 

9  2403.7  2405.6 
65  0  2407.4  2409.3 

1  2411.1  2413,0 

2  2414.8  2416  7 

3  2418.5  2420.4 

4  2422  2  2424  1 

5  2125.9  2127  8 

6  2429.6  2431.5 

7  2433  3  2435,2 

8  2437.0  2438  9 
9!2440.7  2442.3 

66«»2444  4'2446.3 

1  2448  1 1 24.50.0 

2  2151,9  24.5,3,7 

3  245.5.6  2457.4 

4  2459.3  2461.1 
5'2463.0!2464.8 
6'2166.7!2168  5 
7'2470.4'2472  2 
8  2474.1  2475.9 
9'2477.8  2479,6 

e70'2181.5i24s3.3 
l'248.5.2'2487.0 
2  2488.9'2490.7 
3'2192.6'2494.4 

4  2196.3  2498.1 

5  2500.0  2-501.8 

6  2503.712505.0 

7  2,507.4: 2509..3 

8  2511.1  2513,0 

9  2514.8j2516,7 
680  2518.5  2-520.4 


3 
4 
5 
G 
7 
8 
9 

710 
1 

2 
3 
4 
5 


7 
8 
9 

720 
1 
2 
3 


2596.3  2.598.1 
2600,02601.8 
2303.7  ;260.5.6 

2607.4  2309.3 
2611.1,2613,0 
•2614.8  2616.7 

2618.5  2620,4 
2622,2  2624,1 
2625.9  2627. H 
2629  6  2f>31.5 
26,33  3  2635  2 
2637.02638.9 


2640.7 
2644.4 
2648.1 


2642.6 
2646.3 
2650.0 


6  2651  9  26.53. 


2655.6 


26.59.3  2661.1 
2363.0  2664.8 


2366.7 
2670.^ 
2374.1 


2377.8  2679.6 


4  2631.5 

5  2685.2 


6  2688.9  2690 


7,2692.6 


8  2696,3  2698.1 


9:2700.0 
7  3  0  2703. 
1 '2707.4 

2  2711.1 

3  2714.8 


7 
8 
9 
74i) 
1 
2 

3 
4 
5 
6 
7 
8 
9 

750 
1 


2718.5  2720.4 
2724.1 

6  272.5.9  2727.8 

2729.6  2731.5 
2733.3  2735.2 
2737.0  2733.9 


26.57.4 


2668.5 
2372.2 
267.'.,9 


^  .1 


800 
1 
2 
3 


26S3,3 
2687,0 


2694.4 


2701.8 
2705.0 
2709,3 
2713  0 
2716.7 


2740.: 


2748.1 


2742,6 


2744.4  2746.3 


27-50.0 


8 
9 

760 
1 


2188.9  2190.7 
2191,4 


2192.6 

2196.3;2198.1 
2200.0:2201  8 
2203.7 1 2205. 6 
2207.4  2209.3 
7  2211  1  2213.0 
214.8  22:6.7 
9  2218.5  2220.4 
600  2222.2  2224.1 


1 

2522.2  2524,1 

2 

2525,9  2-527.8 

3 

2529  ;  2531.5 

4,2533,3  2535.2 

5  2537.0  2.538.9 

G 

2540  7  2542  (i 

7 

25U.4  2516.;! 

8 

2543  1  2550.0 

9 

2.551.9  25.53.7 

690 

2555.6  2-557.4 

1 

2.559.3  2561.1 

2 

2-563.0  2564.8 

3 

2566,7  2-568.5 

4 

2.570,4  2-572.2 

5 

2.574.1  2.575.9 

S 

2577.8  2579.0 

7 

2581.5  2-583.3 

8 

2585.2  2587.0 

9 

2588.9  2590.7 

700 

2592.6  2594.4 

2751.9  2753.7 
275.5.6  2757.4 
2759.3  2761.1 
2763.02764.8 
2766.712763.5 
2770.4'2772.2 

2774.1  2775.9 
•2777.8  2779.6 
2781.5  2783.3 
278.5.2  2787.0 
2788.9  2790.7 

792.62794.4 

2796.3  2798.1 
2800.0  2-^01.8 

2803.7  2805.6 

2807.4  2809.3 
■2811,1  2813.0 

2814.8  2816.7 

2318.5  2820  4 

2322.2  2824.1 
3  2825.9  2827.8 

•2829  6  2831.5 
5  2833.3  2835.2 
G  2837,0  2838  9 
2840  7  2342.3 
•2814,4  2846.3 
9'2848.1  28.5O.0 
7 70' 235 1. 9  28.53, 
l'23.55.6  28.57.4 
2'23.59  3  286 

3  2863.0  2864.3 

4  2866.7  2868.5 

5  2870.4  2872  2 

6  2874.1  2875.9 

7  2877.8  2879.6 

8  2881.5  28.S3.3 

9  2885.2  2887.0 
780  2888.9  2890 

1  2392.6  2894.4 

2  2896.3  2898.1 

3  2900.0  2901.8 

4  29it3.7  2905.3 
6  2907.4  2909  3 

6  2911.1  2913  0 

7  2914.8  2916,7 

8  291.3.5  2920.4 

9  2922.2  2924. 1 
790  •29'2-5.9  2927.8 

1  2929.6  2931.5 

2  2933.3  2935.2 

3  2937.0  2938  9 

4  2940.7  2942.0 
6  2944.4  2946.3 

6  2943.1  2950.0 

7  2951.9  2953.7 

8  29-55.6  2957.4 

9  2959.3  2961.1 
800  2963.0  2964.8 


4 
5 
G 
7 
8 
9 

810 
J 

2 

3 
4 

{, 
6 
7 
8 
9 

820 
1 


4 
5 
G 
7 
8 
9 

830 
1 
2 
3 
4 
5 
6 
7 
8 
9 


Contents,  | 
Cu.  Yds.  I 


A. 


840 
1 


3107.4 
3111 
3114.8 

2  3118.5 

3  3122.2 


850 
1 


2963.0  2934.8 
2066.7  2968 
2970.4  2972 

2974.1  2975 
•2977.8  2979, 
2931  5  2983,3 
•2985,2  2987 
2988.9  2990. 

2992.6  2994.4 
29^6.3  2998 
.3000.0  3001, 

3003.7  3005, 

3007.4  3009, 
■m\.\  3i'13  0 
,3014.8  3016. 

3018.5  3020.4 

3022.2  3024, 
3025.9  3027.; 

3029.6  3031. 

3033.3  3035 

3037.0  3038. 

3040.7  3042 
3044  4  3043.3 

3018.1  30.50, 
3051.9  30.53, 
3055.6  3057, 

3059.3  3061, 

3063.0  3064. 
3066  7  3068, 

3070.4  3072, 

3074.1  3075. 

3077.8  3079.6 

3081.5  3083 
;?085.2  3037.0 
30^8.9  3090 

3092.6  3094.4 
3096.3  3098. 
3100.0  3101.8 

3103.7  3105.0 


3125.9  3127.8 


3129.6 


6  3133  3  3135,2 
3137.0  3133,9 

8  3140. 

9  3144.4 
3148.1 
3151,9 


3155.6  3157.4 
3  3159.3  3101.1 
3163.0  3164.8 


6  3166.7 


G  3170.4  3172.2 


86 


3174.1 


31093 

3113.0 

3116 

3120.4 

3124.1 


3131.5 


3142.6 
3146.3 
3150.0 
31.53 


3168..^ 


3175. 


3!77.8  3179.U 
3181.531833 


3185.2  3187.0 
3188.93190.7 
3192.63194.4 

3  3196.3  3' 98.1 

4  3^200.0  3201.8 
6  3-203.7 1 3205.(1 

6  3207.4  3209.3 

7  3211.1  3213.0 

8  3214.8|3216 

9  3218  5  3^2^20.1 
870  32-22. 2' 32^24. 1 

1  32-25  9,3-227.8 

2  32.9.6,3231. 

3  3233.3  32;i5. 

4  32,37.o!3238.9 

6  3240  7l321-2.( 
G  3244,4  3246.; 

7  3'248.1  ;^250.0 

8  3251  9:^253 

9  3255.6  3257.4 
8.80  3259.3  3261 

1  3263.0 

2  3266. 


3  3270.4  32 


4:3274.1 
6  3277.8 


6.3281.5  3283.3 


7,3-285.2 


8 '3238.9  3290 


9.3292.6 
89  0  3296.3 


1  3300.0  3301.8 


2  3303.7 

3  3307.4 
4 '33 11.1 
6 13314.8 

;5318.6 
3322.2 
33^5.9 


:?264.8 
3233.5 


3275.9 
3279.6 


3^287.0 


3294  4 
;^'298.1 


9 


900  3333.3  3335.2 


3305.6 
.3309.3 
.3313.0 
3316.7 
;!;i20.4 
3324.1 
3327.8 


3329.6  3331.5 


900 
J 


8 
4 

5 
6 
7 
8 
9 

910 
I 


7 
8 
9 

920 


Contents, 
Cu.  Yds. 


333.3.3  3335  2 

3337.0  3338.9 
3340.7  3342.6 
3344.4  3346.3 

3348.1  3350,0 

:«5i. 9  3.3.53.7 
;«55.6  33.57.4 

3:^59.3  3361.1 

3333.0  3364,8 
9  3366.7  3368.5 

3370  4  3372.2 

3374.1  3375.9 

2  ;«77.8'3379.6 
3:;«81.5  3.383,3 
4  .333.5.2  33.^7.0 
513388.9  3390.7 
6:3392.6  3394  4 

3:«6.3  3398.1 
31(10.0  3401.8 
3403  7  3405,6 
3407.4  3409,3 
1  3411.1  3413,0 
2,;^414.8  3416.7 

3  3418  5  3420,4 

4  34^22.2  34-24.1 

6  342.5.9  34-27  8 
G  3429.6  3431,5 

7  34.33  3  3435,2 

8  3437.0  3438.9 

9  3440.7  3442.6 
930  3144.4  3443.3 

1  3148.1  34.50.0 

2  3151.9  34.53.7 

3  3455.6  3457.4 

4  3459.3  3461.1 

5  3163.0  3464.8 

6  3466.7|3468.5 

7  3470.4  3472.2, 

8  .3474.1  3475.9 

9  ;«77.8, 3479.6 
940  3131.5,3483.3 

1  3485.2  3187.0 

2  3488.9'3490.7 

3  3492.6  3494  4 
4'3493.3  3498.1 
5,3.500.0  3.501.8 
6.3503.713.505.6 
7 ;.3507.4  3.509.3 
8:3511.1  3513.0 
9!3514,8'3516,7 

95O3518.5'3520.4 
1  3522.23524.1 
•.  |3525.9  ;i527.8 

3  3529.6  3531.5 

4  3.533.3  353.5.2 

5  3,537.0  3.5.38.9 
G  3510.7  3-54-2.6 
7 '3541.4  3546.3 

8  3548.1  3550.0 

9  3-551.9  3553,7 
960  3.555.6  3,^57.4 

1  3.5.59.3  3.561  1 

2  3563.0  3504  8 

3  3.566.7  3.')68,5 

4  3570.4  3572  i 

5  3.574.1  3575  9 

6  3577.8  3.579.6 

7  3-581.6  3.583.3 

8  .3.585.2  3587.0 

9  3.588,9  3.590,7 
970  3.592.6  3594,4 

1  3596.3  3598.1 

2  3600.0  3601.8 
8  3603.7  3605.6 
4  3607.4  3609.3 

6  3611.1  3613.0 
G  3614.8  3616.7 

7  3618.5  3620.4 

8  3622.2  3624.1 

9  3625.9  3627.8 
980  3629.6.3631.5 

1  ,363;i3  3335  2 

2  3337.0  3638.9 
3;}610.7  .3612  6 

4  3644.4  3(;i()  3 

5  3648.1  3650.0 

6  3651.9,3653.7 

7  3(>55.6  3(i57,4 

8  .36.59.3  3631,1 

9  366:i,o  ;^(;(;4.8 
990  3666.7  3(!H8.5 


3672.2 
3675.9 


1  3670.4 

2  3674.1 

3  3677.8  3679.6 

4  3681.5|36.S3  3 

5  ,3685.2!3687.0 

6  3688.9  ,3690  7 

7  3692.6  3694.4 

8  3696.3  3698.1 

9  3700.0  3701.8 
100  0  3703.71 


RATIOS  OF  CORRECTION  FOR  AVERACE  END  AREA  CALCULATIONS. 


WIDTH  OF 
UOAI)  UKII. 


Area  of 


1.-J5    2  2.5 


2  12 


2.25   to  100 


14 


100 


16 


18 


100 


100 


20 


100 


22 


100 


24 


100 


26 


28 


100 


100 


30 


100 


H  ifjlit  ..r 


1  1 


1—5 


6.04  5.2  4.74 


5,74  4.81  4.41-5.14  4.45  4.13  4.72  4.14  3.88  4..33  3.87  3.644.00  3.62  3.43 


'i.71  3.43  3.243.47  3.20  3.07  3.24  3.20  2.91 


Ua  in  nt 
Kiiil 
Anas, 


1:1 

1:1.2 

1:1.4 

1:1.6 

1:1.8 

1:2 

l:2.o 

l:;j 

1::5..> 

1:1 

1:4.5 

1:.'» 

1  :'.."> 

1:6 

1:6..> 

1:7 

1:7.5 

l:s 

l:s.5 

1:» 

1:1>.5 

1:10 


.sertion 
Varj  iiij; 
I'll  a  I 
SI -cs. 


Slope. 


}:1 


.001 
.002 
.007 
.012 
.019 
.033 
.045 
.056 
.067 
.076 
.0S5 
.093 
.100 
.107 
.113 
.119 
.124 
.]  28 
.133 
.13S 
.142 


001 
003 
006 
OIO 
014 
023 
032 
Oil 
050 
057 
065 
071 
077 
083 
089 
094 
100 
106 
111 
117 
123 


1:1 


n-.i 


001  .001 
,004  .004 
.007  .00,s 
012.01 
018  .022 
,032  .033 
,043  .044 
,0i5  ,056 
,066  .067 
075  .076 
,083  .084 
,0911.092 
,098 '.100 
105  .106 
110  .111 
115! 116 
120.122 
125|.127 
130M32 
134!. 1,36 
138'. 140 


Slope. 


Slope. 


Slope. 


Slope. 


Slope. 


Slope. 


Slope. 


Slope. 


Slope. 


Slope. 


Ratio  of 
Anas. 


1:1 


,001 
.002 
.004 
.006 
.009 
.016 
.023 
.030 
.0,38 
.043 
,049 
,055 
060 
065 
,070 
075 
079 
,084 
088 
092 
097 


1:1 


,001 
,004 
,006 
010 
.014 
;026 
037 
,047 
,057 
,066 
,074 
,081 
088 
094 
100 
105 
110 
115 
120 
125, 
130 


1^:1 

.001 
.004 
.007 
.011 
.015 
.027 
.040 
.051 
.061 
.070 
.07.S 
.084 
,093 
,099 
,105 
110 
.115 
120 
,125 
,130 
135 


}:1 


.001 
.002 
.003 
.005 
.006 
012 
.019 
.026 
.033 
.039 
.044 
.050 
.055 
.060 
.065' 
.069' 
.073 
.077 
.082 
.0S6 
.090 


1:1 


1^:1 


,001  .001 
,003  .003 


006 
010 


.006 
.010 


.014.014 
.024'.026 
.035  .037 


,045 
,054 


.04 

.056 


062  .065 
,070' 07 
,0771.080 
084'.088 
0901  095 
095'.101 
100|.105 
106'. Ill 
1111.116 
116'. 121 
12l|.125 
126.130 


.001 
.002 
.00:; 
.005 
.010 
.016 
.022 
.029 
.035 
.040 
.046 
.051 
.056 
.060 
.064 
.068 
.072 
.076 
.086 
.084 


1:1 


.001 

.003 
.006 
.010 
.014 
,024 
.033 
.042 
,051 


U:l 


4,1 


.001 
.003 

,00f 

.010 

.014 
.025 
.035 
.047 
.054 


.059  .062 
.066  .070 
.073  .078 
.079  .085 
.085  .091 
,091|.097 
096'. 102 

,101 .107 

106  .112 
,111|.117 
116.121 
120'.126 


.001 
.002 
.003 
.005 
010 
.014 
,020 
,025 
0311 
,036 
,042 
,047 
051 
055 
058 
062 
065 
069 
072 
075 


i-.m-.i 


hi 


,001 .001 

,003  .003 
,00(i  .006 
.009  .00!) 
.013  .013 
.022  .024 
.031L034 
.039  .044 
.048i.052 


.055 
.063 
.070 
.076 
.082 
.088 
.093 
.098 
.102 
.106 
111 
.116 


.060 
.(i6S 
.075 
.082 
.088 
.093 
.098 
.103 
.108 
113 
117 
.122 


,001 
,002 
003 
.005 
010 
,014 


1:1,1^:1 


hi 


1:1 


.001  .001 
.003  .003 
,005  .005 
.008  .009 
,012.013 
020  .023 
,028  .033 
019.037  .042 
.O23L045  .050 


1^:1 


.053  .058 
060  .066 
.066  073 
.072  .079 
.078  .085 
.083  .090 
,053  .088  .095 
056.093.100 
.060  .097  .104 
,063  .102.109 
,066  .106  .113 
,0691.111  .118 


.028 
.033 
.037 
.041 
.045 
.049 


001 
.002 
-003 
.005 
.009 
.014 
.019 
,022 
,026 
,030 
,034 
,037 
041 
044 
047 
,050 
,054 
,057 
060 
063 


.001  .001 
.0031.003 


.005 
.007 
.011 
.019 

026 
.034 
.042 
,049 
,05(1 
,062 
,06  s 
,074 
079 
084 
OSI) 
,094 
,09S 
,103 
,107 


.005 
.OOS 
.013 
.021 
.030 
0!9 
.047 
.055 
(HiL' 
069 
.075 
.081 
.OSO 
.091 
.095 
.100 
,105 
.110 
.114 


1-1 
4.1 


1:1 


 .001 

001 1. 003 
002  .005 
r03  .007 
.005 '.010 
010.017 
013  .025, 
.0171.032 
021 1. 039 
024.046 
.028  .053 
,031  .059 
,034  .064 
037  .070 
040  .075 
043  .080 
047  .084 
0.50  08S 
053  .093 
056  .098 
059  .102 


U:l 

.001 
.003 
.005 
.00 
.012 
.020 
.028 
.036 
.045 
.052 
.059 
.066 
.07-/ 
.077 
.082 
.0>7 
.092 
.097 
.lul 
.lO'v 
110 


1:1 


001 
,002 
003 
005 
,008 
012 
016 
019 
022 
025 
028 
031 
034 
037 
040 
043 
046 
048 
051 
054 


1:1 


,001 
.002 
.004 
.006 
009 
016 
.023 
.030 
037 
044 
.050 
055 
.060 
065 
070 
075 
080 
084 
088 
.(i93 
097 


1J:1 

.001 
.003 
.005 
.008 
.011 

019 
.02' 
.034 
.042 
.050 
.057 
.063 

069 
.075 
.O.SO 
.085 
.0M9 
.091 
.098 
.102 
.107 


hV  1:1  1^1 


.001  .001 
.002  .002 
.004  .005 
.006  .007 
.009  .010 
.015  .018 
.022  .025 
.029  .033 
.03"^  .040 
.041  .048 
.018  .054 
.053  .000 


hi 


001 
,001 
,002 
,003 
,006 
010 
013 
016 
019 
022 
025 
027 
030 
033 
036 
03  S 
041 
044 
046 
049 


001 
001 
002 
O03 
005 
008 
.011 
014 
016 
.019 
021 


l:l'l]:l 


,058 
,063 
067 


.066 
072 
.077 


.O72L082 
.076'.086 
.080.091 
.084  .095 
.088  ,100 
.092  .104 


.001 '.001 
.002  .00-; 
.004  .005 
.006  .00 
.008  .010 
.014.017 
021  .024 
.027  .(*32 
.(•34  .03H 
040  ,046 
.045  .052 
050  .058 
024  .055  .064 
I '26  .060  .069 
029  .064  .074 
031  .068  079 
034  .072  .084 
036  .076  .0S8 
039  .079  .092 
04  i  .083  .096 
044  .087  .100 


1:1 

1:1.2 

1:1.4 

1:1.6 

1:1.8 

1:2 

1:2.5 

1:;{ 

1:3.5 

1:4 

1:4.5 

1:.> 

1:5.5 

1:6 

1:6.5 

1:7 

1:7.5 

1:8 

l:-i.5 

1:!) 

1:1).  5 

I:m) 


On  Estimating  Earthwork, 

The  accompanying  table  is  designed  to 
fiicilitate  the  cuinputation  of  earthwork 
after  the  areas  of  the  cross  sections  have 
been  obtaine(l.  The  areas  may  be  ob- 
tained bv  calculation  from  the  field  notes  ; 
or  the  cross  sections  may  be  plotted  and 
the  areas  obtained  by  the  plani meter. 
'J'iie  firmer  method  is  short  and  easy  in 
a  level  country,  but  where  the  surface  of 
the  ground  is  broken  and  irregular  the 
latter  method  is  to  be  preferred.  Plotting 
tlie  cross  s 'ctions  also  makes  a  complete 
record  of  the  work,  with  its  classification 
at  every  point,  and  allows  revision  atid 
deviation  within  the  limits  to  wiiich  the 
section  is  taken,  by  simply  indicating  the 
position  of  the  centre  line.  Usua'iy  it 
will  be  found  easiest  to  plot  the  rods 
fri>m  a  line  assumed  as  the  height  of  in- 
strument ;  but  when  the  work  is  extend- 
ed so  as  to  involve  several  heights  of 
instrument  in  the  same  section,  or  when 
the  work  is  to  be  used  for  a  great  i.i.mber 
of  calculations  tor  successive  estimates, 
it  will  be  found  cheapest  to  work  from 
elevations. 

A  convenient  form  for  the  estimate 
sheets  is  here  sliown.  In  the  two  first 
columns  are  entered  the  stations  and 
plus-es  at  which  the  cross  sections  are 
tiiken.  The  column  headed  "'Length  in 
Feet"  is  filled  up  by  subtracting  the 
numbers  in  these  two  first  coluinns.  The 
columns  headed  "  Area  uf  Cross  /Section  " 
are  filkd  up  with  areas  obtained  either 
from  calculation  or  from  measurement 
by  the  planimeter.  In  the  columns  head- 
ed "Aventcje  Area"  are  entered  one-half 
the  sums  of  the  areas  of  adjacent  cross 
sections.  If  preferred  the  suras,  in.^tead 
of  the  halt'  sums,  may  be  used,  in  which 
case  the  final  contents  will  be  doubled. 

The  main  columns  of  "  Contents  in 
Cubic  yards  ^'  are  now  filled  up  by  aid 
of  acc(mipanying  "  Table  of  Cubic  Yards 
in  Lengths  of  lUO  Feet."  If  the  lengths 
are  li'O  feet  the  corresponding  quantities 
are  si 01  ply  transferred  from  the  table.  If 
the  distance  is  50  feet,  one  half  the  quan- 
tity is  transferred.  If  the  distance  is  25 
feet,  one-fourth,  &c.  Usually  the  opera- 
tion can  be  performed  mentally.  The 
table  being  set  up  before  one,  the  arrange- 
ment of  it  is  such  that  the  eye  knows  just 
wlvere  to  strike  for  a  quantity.  There 
are  no  leaves  to  turn.  Quantities  can  be 
entered  as  fast  as  one  can  write.  Blue 
ink  may  be  used  in  writing  quantities  in 
excavati'Mi,  and  red  ink  in  writing  quan- 
tities iu  embankment. 

The  calculation  of  earthwork  by  the 
metiiod  of  averaging  end  areas  is  not 
theoretically  correct,  excepting  in  the 
two  special  cases :   one  when  the  end 


areas  are  equal,  and  the  other  when  the 
prismoid  has  two  of  its  longitudinal 
bounding  planes  parallel.  As  that  por- 
tion of  every  roadway  prismoid,  which 
lies  between  the  vertical  planes  passing 
through  the  edges  of  the  roadbed  is 
practically  included  in  the  latter  condi- 
tion, it  follows  that  the  variation  from 
the  true  contents,  obtained  from  averag- 
ing end  areas,  lies  outride  the  central 
roadbed  prism,  and  we  may  consider  it  as 
dependent  on  the  four  following  factors : 

1st.  The  ratio  of  the  end  areas  of  the 
prismoid. 

2nd.    The  width  of  the  roadbed. 
3rd.    The  degree  of  the  slope. 
4th.    The  heighth  of  the  section. 

This  variation  has  been  investigated 
with  the  result  shown  in  the  table  called 
" Itutios  of  Correction  for  Average  End 
Area  Calculations."  The  manner  of  pro- 
ceeding was  briefly  thus :  With  the  data 
shown  in  the  heads  of  the  columns  in 
the  table,  and  in  the  left  hand  column, 
the  true  contents  of  the  prisms  by  the 
prismoidal  fi)rmula  were  found,  as  well 
as  the  contents,  by  averaging  end  areas. 
The  ratio  of  variation  in  many  par- 
ticular cases  being  thus  found,  the  curve 
of  variation  for  each  class  was  formed 
by  measuring  the  ratios  of  end  areas 
on  the  axis  of  abscissas,  and  the  per- 
centages of  variation  on  the  axis  of  ordin- 
ates.  Some  maxima  and  miruma  of  these 
curves  were  also  traced,  which  seemed 
to  differ,  in  extreme  cases,  10  per  cent,  or 
so  from  the  mean  given  in  the  table.  It 
is  believed  these  deviations  will  usually 
counterbalance  one  another.  If  the  work 
is  of  a  ])eculiar  nature,  so  the  general 
cases  here  worked  out  will  not  apply,  cor- 
rections applying  to  it  can  be  worked  out 
and  entered  in  one  of  the  blank  columns. 

To  apply  the  table  of  corrections,  we 
divide  one  area  of  cross  section  by  its 
neighbor,  and  take  from  the  table  its  cor- 
responding ratio  or  percentage  of  correc- 
tion and  multiply  the  contents  by  it, 
writing  the  result  in  the  column  headed 
"  Correction."  The  special  case,  when 
one  end  is  zero,  or  ends  at  grade,  is  not 
provided  for  in  table  of  corrections.  For 
this  case  the  correction  is,  the  slope  area 
multiplied  by  one  sixth  the  length.  For 
the  road  bed  area  being  the  base  of  a 
wedge,  the  solidity  is  one-half  base  niulti- 
plied  by  altitude;  but  the  slope  areas  being 
bases  of  pyramids,  the  solidity  is  one-third 
base  multiplied  by  altitude.  One  half 
which  is  used,  less  one-third,  which 
should  be  used,  equals  the  correction,  one- 
sixth.  This  correction,  as  well  as  all 
others,  is  to  be  deducted  from  contents  in 
main  column. 


Estimxted  duantities  in  Grading, 


STA- 

TIO.NS 


No. 


+ 


AUEA  OF  CROSS 
IN  S({U\KK  I^T. 


AVEKAOE  AREA. 


Excavation, 


117 
118 


119 


120 


121 


122 
123 


50  Cut comnec'ces 

....I  18  16 

50158  53105. 
....63o'l63325 


526 
595 


50638 263 
854171297 
....'110243485 
20  Cttl 
40 

60  31 
80103 


Cut  coin  men  ces  68 


....'334280  560 


,35700  27 
•50743157 


..'821 

,30534 
61|  cut 

70  

84  1 

90  mtl 


ends 


50870156  209 


1«7 


ends 


Eni- 
baiik' 
meut 


300 

314 


255 


3147 


com  men  ces 


.394 
634 
527.1 
263.', 
55' 


15J 
72 
218^ 
517 
52  H 

m\ 

845J 
677  J 
267" 


=  3 


341 
108 
212 
280 
270 
121^ 


170 
278^ 
217 
156.1 
17U 
130 
36J 


15 
67^ 
215,! 
426 
560^ 
540 
242^ 


280 
557  ^ 
434l 
26  H 
232 
201 
73A 


Em- 
bank 
ment 


Corrected  Totals, 


CONTENTS  IN  CUBIC  YARDS. 


Kxcaralion. 


16.7  1 
162.916 
729.632 
1174.1 
683.8 
136  3 
40.7 


11.4 

53.3 

161.9 

670, 

400  S 
2987.0 
1565 

752.8 

306.518 


9S53.7  98 


9755.71....  2922.4 


14  8 
63.9 
200.6 
394  4 
362.9 
150  0 
90.0 


103.7 
361.0 
120  6 
579  6 
317.6 
144.4 
41.9 


2945.423 


:z  u 


27.8 
125.0 
399.1 
788.9 
626.5 
300.0 
179.6 


207.4 

722, 
241.3 
96S.5 
4296 
223.3 
84.4 


Em 
liaiik- 
mi'Ul 


25.1 
25.1 


7.6 
23.8 
.5.1 


461  86.' 


5278.1  82.7 


UEUARKS. 


The  error  from  calculation  by  averag- 
ing end  areas  is  not  so  great  as  appears 
at  first  sight,  or  as  it  is  often  represented. 
Taking  isolated  cases,  where  the  ratio  of 
end  areas  is  great,  it  may  be  made  to 
appear  that  the  error  is  10  or  15  per  cent.; 
but  taking  extended  work  the  whole 
error  is  trifling,  the  great  bulk  of  con- 
secutive cross  sections  being  nearly  equal 
to  each  other,  and  the  errors  are  distri- 
buted. The  writer  tested  one  section  of 
28,(j0  >  cu.  yds.  and  f  )und  the  error  less 
than  one  third  of  one  per  cent.  What 
appeared  to  be  a  sectitm  which  would 
show  great  error  on  account  of  crossing 
several  short  ravines  and  gullies,  con- 
taining some  85.000  cu.  yd.s.,  was  less  than 
one-half  of  one  per  cent,  out  of  the  way. 

In  earthwork  there  are  only  two  sides 
of  the  prismoid  perfect  planes,  and  these 
two  are  the  thecjretical  planes  of  the 
cross  section.  The  surface  of  the  ground 
is  never  a  perfect  plane.  The  rod,  in 
taking  points  usually  sinks  a  little  in  the 
ground,  the  slopes  are  not  trimmed  exact- 
ly, nor  the  grade  made  perf  ct.  If  there 
is  any  difference  between  the  true  so'i  lity 
and  that  obtained  by  the  method  here 
presented,  it  is  the  conviction  of  the 
writer  that  it  would  be  easier  and  cheap- 
er for  the  engineer  to  shovel  it  than  to 
calculate  it. 

The  method  of  calculation  for  earth- 
work should  be  direct  and  simple,  so  it 
can  be  used  safely  by  assistants  not  speci- 


ally skilled  in  intricate  calculations..  It 
is  better  for  the  engineer  to  spend  much 
of  his  time  in  the  field,  minutely  observ- 
ing and  closely  measuring  the  work,  than 
to  spend  it  mainly  in  the  ofl!ice,  basing 
refined  computations  on  erroneous  or 
careless  measurenieiits.  The  cri-ors  in 
measurement  will  usually  be  greater  than 
the  errors  of  calculation,  by  averaging 
end  areas  without  cori'ection. 


— Pulili.^lied  by— 

JOHN  WILEY  &  SONS, 
Scientific?  I*  iil>lisliers 


1.5  Astor  Place. 


NEW  YORK  CITY. 


The  New  and  Complete  Catalogue 

OF  THE  PUBTjIOATIONS  OF 

JOH]\  WIIiEY  &  5?;OIVS, 

IS  Astor  Place,  New  York, 
CONTAINING 

Scientific  and  other  Text  Books 

FOR 

COILEGES,  INDCSTRHL  SCHOOLS  k  THEOLOGIC.U  SEJUNARIES, 

with  many  valuable  practical  works  for 

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INCLUDING  WORKS  ON 
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THEOLOGICAL  SEMINAKIES, 
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also  a  full  list  of  their  editions  of 

JOHN    RUSKIN'S  WORKS. 

Will  be  sent  free  by  mail  lo  anyone  ordering  it. 


TABLE  OF  CUBIC  YARDS  IN  LENGTHS  OF  100  FEET 

ADAPTED  ESPECIALLY  TO  THE  CALCULATION  OF  EARTH  WORK  BY  THE  METHOD  OF  AYERAGING  EXD  AREAS. 


Contenis  of  Column  "A"  are  for  the  integers  in  column  headed  "Area,  Square  Feet." 
Contentti  of  Column  "  B  "  are  for  the  same  integers  plus  0.5  square  foot. 


COPYRIGHT  1885  BY  S.  B.  FISHER. 


Contents  for  lengths  greater  or  less  than  100  are  obtained  by  simple  proportion,  thus:  125 
sq.  ft.  for  length  of  20  {l.=ja%^i  of  463.0  cu.  yd;.;  the  contents  for  125  sq.  ft.=92.6  cu.yds. 


Cont'-pts, 
Cu.  Yds. 


1 

2 
3 
4 
5 
6 
7 
S 
9 
10 
1 
2 
3 
4 
5 
6 


20 


30 


40 


B. 


8 
9 

50 
J 
2 
3 
4 
5 
G 
7 
8 
9 

CO 
1 
2 
3 
4 
5 
C 
7 
8 
9 

70 
1 
2 
H 
4 
5 
6 
7 
8 
9 

80 
1 
2 
3 
4 
6 
6 
7 
8 
9 

90 
1 
2 
3 
4 
5 
6 
7 
8 
9 

10(1 


3.7 
7.4 

II.  l 
14.8 
18.5 
22.2 
2.^.9 
29.»i 
33.3 
37.0 
40.7 
44.4 
48.1 
51.9 
55.6 
59.3 
63.0 
66.7 
70.4 
74.1 
77.8 
81.5 
85.2 
88.9 
92  6 
96.3 

1000 
103.7 
107.4 

III.  l 
114.8 
118.r- 
122.2 
12.5.9 
129.0 

107.0 

140.7 

144.4 

143  1 

151.9 

155.6 

159.3 

103.0 

16G.7 

170.4 

174.1 

177.8 

131 

135.2 

13S.9 

192  6 

193.3 

200.0 

203.7 

207.4 

211.1 

214.8 

218.5 

222  2 

225.9 

229.6 

233.3 

237.0 

210  7 

214.4 

218.1 

251.9 

2'>5.6 

2.59. 3 

2il3  0 

266  7 

270.4 

274.1 

277.8 

23 1. 5 

285.2 

288.9 

292  6 

296  3 

300.0 

3i)3.7 

307.4 

311.1 

314.8 

318.5 

322.2 

325.9 

329.6 

333.3 

337.0 

310.7 

344.4 

318  1 

351.9 

3")5.6 

359.3 

363.0 

366.7 

370.4 


1.8 

6.6 
9.3 
13.0 
16.7 
20.4 
24.1 
27.8 
31.5 
35.2 
38.9 
42.6 
46.3 
50.0 
53.7 
57.4 
61.1 
618 
68.5 
72  2 
75.9 
79.6 
83.3 
87.0 
907 
94.4 
98.1 
101  8 
105.6 
109.3 
113.0 
116 
120.4 
124.1 
127.8 
131 
135.2 
1339 
142.6 
1433 
150.0 
153.7 
157.4 
161.1 
161.8 
163.5 
172.2 
175,9 
179.6 
183  3 
1S7.0 
190. 
191.4 
19il 
201.8 
20 
209.3 
213.0 
216.7 
220. 
221.1 
227.8 
231.5 
235.2 
238.9 
242.6 
246.3 
250.0 
253.7 
257.4 
261.1 
264.8 
26S.5 
272.2 
275.9 
279.6 
283.3 
287. 0 
290.7 
294.4 
298 
301.8 
305.6 
309.3 
313.0 
316.7 
32i).4 
324 
327.8 
.331 
335.2 
338.9 
342.6 
346.3 
350.0 
353.7 
357,4 
361. 
364.8 
368.5 
372.2 


Coateiits, 
Cu.  Yds. 


A.  B. 


100 
1 

2 
3 
4 
5 
6 
7 
8 
9 
110 
1 
2 
3 
4 

6 
7 
8 
9 
120 
1 
2 
3 
4 

6 
7 
8 
9 

130 
1 
2 
3 
4 


9 
140 
1 

2 
3 
4 

5 
6 
7 

8 
9 

loO 
1 

2 
3 
4 
5 
6 


9 

160 
] 
2 
3 
4 
5 
6 
7 
8 
9 

17*. 
1 

S: 
3 
4 
5 
(( 
7 
8 
i> 

180 
) 
2 
3 
4 
5 
6 
7 
8 
9 

190 
1 

2 
3 
4 
5 
6 
7 
8 
9 

200 


370.4 
374.1 
377.8 
381.5 
385.2 
388.9 
392.6 
396  3 
400.0 
403.7 
407.4 
411.1 
414.8 
418  5 
422  2 
425.9 
429  6 
•433  3 
437.0 
440  7 
444.4 
448  1 
451.9 
455  6 
459  3 
463.0 
466  7 
470.4 
474.1 
477.8 
481.5 
485.2 
488.9 
492.6 
496.3 
500.0 
503.7 
507.4 
511.1 
514.8 
518.5 
522  2 
525.9 
529.6 
533.3 
537  0 
540.7 
544.4 
543.1 
551.9 
555.0 

559  3 
563.0 

560  7 
570.4 
574.1 
•577.8 
581.5 
585.2 
538.9 
592  6 
5963 
600.0 
603  7 
607.4 
611.1 
014.8 
018.5 
022.2 
025  9 
629.0 
633.3 
637.0 
610  7 
044  4 
048.1 
651.9 
655  6 
659.3 
663  0 
666.7 
670.4 
674  1 
677.8 
681  5 
685.2 
688.9 
092.6 
696.3 
700.0 
703.7 
707.4 
711.1 
714.8 
718.5 
722  2 
725.9 
729  6 
733  3 
737.0 
740.7 


372.2 
375.9 
379.6 
383.3 
387.0 
.390.7 
394.4 
39S.1 
401.8 
405.6 

409.:h 

413.0 
416.7 
420.4 
421.1 
427.8 
431.5 
435.2 
438  9 
442.0 
446.3 
450.0 
453.7 
457.4 
461.1 
404.8 
468,5 
472.2 
475.9 
479.6 
483  3 
487.0 
490  7 
494.4 
493.1 
501.8 
505.0 
509.3 
513.0 
510.7 
520.4 
521.1 
527.8 
531.5 
535.2 
533.9 
542.6 
546.3 
550.0 
553.7 
557.4 
561.1 
564.8 
563  5 
572  2 
575.9 
579.6 
583.3 
587.0 
590.7 


Conteiiis, 
Cu.  \iU. 


200 
1 

2 
3 
4 
5 
6 
7 
8 
9 

2K' 
1 
2 
3 
4 
5 
0 
7 
8 
9 

220 
1 
2 
3 
4 

6 
7 
8 
9 

230 
1 
2 
3 
4 

a 

6 
7 
8 
9 

240 
1 
2 
3 
4 
5 
G 
7 
8 
9 

230 
1 
2 
3 
4 
5 
0 
7 
8 
9 


CoiitfUis, 
Cu.  Yds. 


594  4  260 

598.1 


0018 
005  6 
609.3 
613.0 
016.7 
620.4 
6241 
627.8 
031.5 
635.2 
638.9 
642.6 
640.3 
650.0 
653.; 
6>7.4 
661  1 
664.8 
668.5 
0722 
675.9 
679.6 
683.3 
687.0 
690.7 
694.4 
698.1 
701.8 
705.6 
709.3 
713.0 
716.7 
'^20.4 
724.1 
727.8 
731.5 
735.2 
738.9 
742.6 


740.7 
744.4 
748,1 
751.9 
755,0 
759.3 
763  0 
766  7 
770.4 
774  1 
777.8 
781.5 
785.2 
788.9 
792.6 
796.3 
80r.O 
803.7 
807.4 
811.1 
814.8 
818.5 
822,2 
825,9 
829.6 
833.3 
837.0 
840.7 
844.4 
843.1 
851.9 
855.6 
859.3 
863.0 
806.7 
870  4 
874.1 
877.8 
881.5 
835.2 
883  9 
892.6 
803.3 
900  0 
903.7 
907.4 
911.1 
914.8 
918.5 
922  2 
925  9 
92D.6 
935  3 
937.0 
94).7 
914.4 
948.1 
951.9 
955  6 
959.3 
903.U 
966  7 
970  4 
974.1 
977.8 
931.5 
985.2 
988  9 
992.6 
996.3 
27i»  1000.0  1001.8 

1  1003.7  1005.6 

2  1007,4  1009.3 

3  1011.1  1013.0 

4  1014.8  1016.7 
6  1018.5  1020.4 

6  1022.2  1024.1 

7  1025.9  1027.8 

8  1029.6  1031.5 

9  1033.3  1035.2 
280  1037.0  1038.9 

1  1040.7  1042.3 

2  1044.4  1046  3 

3  1048.1  1050.0 

4  1051.9  1053.7 
6  1055.6  1057.4 

6  1059  3  1061.1 

7  1063.0  1064.8 

8  1066,7  1068.5 

9  1070.4  1072.2 


742.6  . 

7463 

750  0 

753.7 

757.4 

761.1 

764,8 

768.5 

772  2 

775.9 

779.6 

783.3 

787.0 

790.7 

794.4 

798.1 

801.8 

805.6 

809.3 

813.0 

816.7 

820.4 

824,1 

827.8 

831.5 

835.2 

838.9 

842.0 

843  3 

850.0 

853.7 

857.4 

861.1 

864.8 

863  5 

872  2 

875.9 

879.0 

883.3 

887.0 

890.7 

891.4 

893.1 

901.8 

9(15.0 

909.3 

913.0 

910.7 

920.4 

924.1 

927.8 

931.5 

935.2 

933.9 

942.6 

946.3 

950.0 

953.7 

957,4 

961.1 

964,8 

938.5 

972.2 

975.9 

979.6 

983.3 

987.0 

990.7 

994.4 

998  1 


300 
1 
2 
3 
4 
6 
6 
7 
8 
9 

310 
1 
2 
3 
4 
5 

7 
8 
9 

320 
J 
2 
3 
4 
6 
6 
7 
8 
9 

33<i 
1 
2 
3 
4 
5 
6 
7 


A. 


29>)  1074.1 
1,1077.8 


2  1081-51083.3 


4 
5 
6 
7 
8 
9 

300 


1085.2 
1 088.9 
1092.6 
1096.3 
1100.0 
1103.7 
1107.4 
1111.1 


1075.9 
1079.6 


1087.0 
1090.7 
1094.4 
1098.1 
1101.8 
1105.6 
1109.3 
1113.0 


9 
340 
I 

2 
3 
4' 
5 
6 
7 
8 
9 

350 
1 
2 
3 
4 
5 
6 
7 
8 
9 

360 
1 
2 
3 
4 
5 
6 
7 
8 
9 

370 
1 
2 
3 
4 


1111,1 
1114.8 
1118.5 
1122.2 
1125.9 
U-i9.6 
1133.3 
1137.U 
1140.7 
1144.4 
1148  1 
1151.9 
1155  6 
1159  3 
1163.0 
1166.7 
1170.4 
1174.1 
1177.8 
1181.5 
1185.2 
1188  9 
1192.6 
1196.3 
1200  0 
1203.7 
12>I7.4 
1211.1 
1214.8 
1218  5 
1222.2 
1225.9 
1229.6 
1233.3 
1237.0 
1240.7 
1244.4 
1248  1 
1251.9 
1255.6 


1113.0 
1  1167 
1120.4 
1124.1 

ir/7  8 

1131.5 
1135.2 
1138.9 
1142.  i 
1146.3 
1150.<l 
1 153  7 
1157.4 
1161.1 
1164.8 
1168.5 
1172.2 
1175  9 
1179.6 
1183  3 
1187.0 
1190 
11944 
1198.1 
1201.8 
1205.0 
1209.3 
1213.0 
1216.7 
1 220.4 
1224.1 
1227.8 
1231.5 
12.35.2 
1238.9 
1242.0 
1246.3 
1250  0 
1253.7 
1257.4 


rontfuts, 
Cu.  Yds. 


A.  B. 


400 
1 
2 
3 
4 
5 
6 
7 
8 
9 

41*1 
1 


1259.3  1261.1 
1233.0  1264  8 


9 

3S0 
1 
2 
3 
4 
5 
6 
7 
8 
9 

390 
1 
2 
3 
4 
5 
6 
7 
8 
9 


1266.7 

1270.4 

1274.1 

1277.8 

128 1.5 

1285.2 

1288.9 

1 .92.6 

1290.3 

1300.0 

1303.7 

1307.4 

1311.1 

1314.8 

1318.5 

1322  2 

1325.9 

1329.6 

1333,3 

1337.(t 

1340.7 

1344.4 

1348.1 

1351.9 

1355.6 

1359.3 

1363.0 

1366.7 

1370.4 

1374.1 

1377.8 

1381.5 

1385.2 

1388.9 

1392.6 

1396.3 

1400.0 

1403. 

1407.4 

1.411.1 

1414.8 

1418.5 

1422.2 

1425.9 

1429.6 

1433.3 

1437.0 

1440.7 

1444.4 

1448.1 


1 208.." 

1272.- 

1275.9 

1279  6 

1233.3 

1287.0 

1290.7 

1294.4 

1298.1 

1.301.8 

1305.0 

1309.3 

1313.0 

1316.7 

1320.4 

1324.1 

1.327.8 

1331  5 

1335.2 

1338.9 

1342.0 

1346  3 

1350.0 

1353.7 

1357.4 

1361  1 

1364.8 

1368.5 

1372.2 

1375.9 

1379.6 

1383.3 

1387.0 

1390.7 

1394.4 

1398  1 

1401.8 

1405.<> 

1409.3 

1413.0 

1416.7 

1420  4 

1424.1 

1427.8 

1431.5 

1435.2 

1438.9 

1442.6 

1446.3 

1450.0 


1451.9' 1453.7 
1455  6  1457.4 

1459.3  1461.1 

1463.0  1464,8 

1466.7  1468.5 

1470.4  1472.2 

1474.1  1475.9 

1477.8  1479.0 


2 
3 
4 
5 
*  6 
7 
8 
9 

42<* 
1 

2 
3 
4 

5 
6 
7 
8 
9 

430 
1 

2 
3 
4 
J> 
6 


9 

440 
1 

,2 
3 


400  1481.5  1483.3 


1481.5 
1485.2 
1488.9 
1492.6 
1496.3 
1500.0 
1503  7 
1507.4 
1511  1 
1514.8 
1518.5 
1522  2 
1525  9 
1529  6 
1533.3 
1537.0 
1540.7 
1544.4 
1543.1 
1.551.9 
1.555  6 
1559.3 
1563.0 
1.506.7 
1570.4 
1574.1 
1577.8 
1581.5 
1585.2 
1588.9 
1592.6 
1596.3 
1600.0 
1603.7 
1607.4 
1611.1 
16148 
1618.5 
1622.2 
1625.9 
1629  6 
16.33.3 
1637.0 
1040.7 
4' 1644.4 
6  1648.1 


6 
7 
8 
9 

450 
1 
2 
3 
4 
5 
6 


1651.9 
1655.6 
1659.3 
1663.0 
1666.7 
1670.4 
1674.1 
1677.8 
1681.5 


9 
4Go 
1 
2 
3 
4 
5 
6 
7 
8 
9 

470 
1 

2 
3 
4 
5 
6 
7 
8 
9 

4S0 
1 
2 
3 
4 
5 
6 
7 
8 
9 

490 
1 

2 
3 


1483  3 
1487.0 
1490.7 
1494  4 
1493.1 
1501.8 
1505.6 
1509.3 
1513.0 
1516.7 
1520.4 
1524.1 
1.527.8 
1.531.5 
1535.2 
1,538.9 
1542.6 
1546.3 
1550.0 
1553.7 
1557.4 
1.561.1 
1.564.8 
1568.5 
1572.2 
1575.9 
1579.6 
1583.3 
1587.0 
1590.7 
1594.4 
1598.1 
1601.8 
1605.6 
1609.3 
1613.0 
1616.7 
1620.4 
1624  1 
1627.8 
1631.5 
1635.2 
1638.9 
1642.6 
1646.3 
1650.0 
1653.7 
1657.4 
1661.1 
1664.8 
1668.5 
1672.2 
1675.9 
1079.6 
1683.3 


1685.2  1687.0 


1688.9 
1692.6 
1696.3 


1700.0  1701.8 


1703.7 


1707.4  1709.3 
1711.1 
1714.8 


1722.2 


1729.6 
1733.3 
1737.0 
1740.7 
1744.4 
1748.1 
1751.9 
1755.6 
1759  3 


1690.7 
1694  4 
1698.1 


1705.6 


1713.0 
1716.7 
1718.5  1720.4 


1724.1 


1725.9  1727.8 


1731.5 
1735-2 
1738.9 
1742.6 
1746.3 
1750.0 
1753.7 
1757.4 
1761.1 


17630  1764.8 


1766.7 
1770.4 
1774.1 
1777.8 
1781.5 
1785.2 


1792,6 
1796.3 
1800.0 
1803.7 
1807.4 
1811.1 
1814  8 
1818.5 
1822.2 
1825.9 

4  1829.6 

5  1833  3 

6  1837.0 

7  1840.7 
8-1844.4 
9  1848.1 

600,1851.9 


1768.5 
1772  2 
1775.9 
1779,6 
1783.3 
1787.0 


1788.9  1790.7 
1794.4 
1798.1 
1801.8 
1805,0 
1809.3 
1813.0 
1816.7 
1820.4 
1824.1 
1827.S 
1831.5 
1835.2 
1838.9 
1842.6 
1846.3 
1850.0 


1853.7 


Contonts, 
Cu.  Y>U. 


500 
1 
2 
3 
4 
5 
6 
7 
8 
9 

510 
1 
2 
3 
4 

b 

6 
7 
8 
9 

520 
1 
2 
3 
4 
5 
6 
7 
8 
9 

530 
1 
2 
3 
4 

r, 

6 
7 
8 
9 
ilO 
1 
2 

3 
4 


1851.9 
1855.6 
1859.3 
1863.0 
1866  7 
1870.4 
1874.1 
1877.8 
1381.5 
1885.2 
1888-9 
1892.6 
1896.3 
1900  0 
1903.7 
1907.4 
1911.1 
1914.8 
1918.5 
1922  2 
1925,9 
1929.6 
1933.3 
1937  0 
1940.7 
1944.4 
1948.1 
1951.9 
1955.6 
1959.3 
1963.0 
1963.7 
1970.4 
1974.1 
1977.8 
1981.5 


18-53.7 
1857.4 
1861.1 
1864.8 
868.5 
1872.-' 
1875.9 
1879.6 
1883.3 
1887.0 
1890  7 
1894.4 
1898.1 
1901.8 
1905.6 
1909.3 
1913.0 
1916.7 
1920.4 
1924.1 
1927.8 
1931.5 
1935.2 
1938.9 
1942.6 
1946.3 
19.=v0.0 
1953.7 
1957.4 
1961.1 
1964.8 
1968..^ 
1972.2 
1975.9 
1979.6 
1983  3 


Contents, 
Cu.  Yds. 


B. 


GOO  22-22.2  2224  1 
l!2-22").9!2227.8 

2  2J-29.6j2231.5 

3  2233  3  2235.2 


Conpnts, 
Cu.  Yds. 


A. 


2-233.9 
2242.6 
22 16.3 
2250.0 
2253  7 
22.57.4 
2-261.1 
2264.S 
2-268.5 
2-272.2 
2275.9 
2279.3 
2-283.3 
2287.0 


1985.2  1987.0 
1988.9  1990.7 
1992.6  1994.1 


1996.3 
-2000.0 
2003.7 
2007.4 
2011.1 
2014.8 
2013.5 
2022.2 


2025.9  2027.8 


550 
1 
2 
3 
4 
b 
6 
7 
8 
9 

56(» 
1 

2 
3 
4 

6 
6 


2029.6 
1033.3 
•2037.0 
2040.7 
2044.4 
2048.1 
2051.9 
2055.6 


-2059.3  2061  1 


•2063.0 


2066.712068.5 
■2070.4  2072.2 
2074.1  2075.9 
2077.8  2079.6 
2081  5  2083.H 
2085.22087.0 
2088  9  2090.7 
•2092  6-2094.4 
2096.3  2098.1 
2100.0  2101.8 


9 

570 
1 
2 
3 
4 
b 
6 
7 
8 
9 

580 
1 

2 
3 
4 

6 
G 


9 

590 
J 
2 
3 
4 
b 
G 
7 


600 


1993.1 
2001.8 
2005.0 
2009,:: 
2013.0 
2016.7 
2020.4 
•2024.1 


2031,5 
2035.2 
2033  9 
2042.6 
2046...! 
2050.0 
2U53.7 
2057.4 


2064  8 


4  2237.0 

5  2240.7 

6  2244.4 
712-248.1 
8'2251.9 
9  2255.6 

610,2259.3 

1  2263  0 

2  2266.7 

3  2-270.4 

4  -2274.1 
6  -2-277.8 
6-2281.5 
7!2i85  2, 
8  -2238  9  2290.7 
9 '2292.6  2294.4 

620  2-296.3 -2-298.1 

1  2300.0  2301.8 

2  2303.7  2305,0 

3  2307.4-2309.3 

4  2311.l|23I3.0 

6  2314  8  2316  7 
6-2318  5  2320.4 

7  232-2.2  2324.1 

8  2325  9  2327.8 

9  23-29.6 '233 1.5] 
630  2333.3  23.35.2 

1  2337.0  233 -t.9 
2-2340.7,2342  0 
3  2344.4  2343.3 
4-2348.1  23.50.0 
6  '2.351.9  2353.7 

6  2355,6  '2357.4 

7  2359.3  2361.1 

8  2363.0  2364.8 

9  2366.7  '2368.5 
640  '2370.4  '2372.2 

1  2374.1  2375.9 

2  '2377.8  2379.6 

3  2331.5  2383.3 
"■4  2.335.2  2387.0 

5  '2388.9  2390.7 

6  2392.6  2394.4 

7  '2396.3  2393.1 

8  2400.0  2401.8 

9  2403.7  2405.0 
650  2407.4  2409.3 

1  2411.1  2413.0 

2  '2414.8'2416  7 

3  '2418.5  24-20.4 

4  2422  2  24-24  1 

6  2425.9  21-27  8 
6 '2429.6 '243 1.5 

7  2433  3  2435.2 

8  2437.0,2438  9 
9'-2440.7|'244'2.6 

660  2444  4  2446.3 


7  .)0  2502.6  259 1.4 
1 -i.V.tC,.:;  '259S.I 
2, '2000,0  -2001.8 
3|'2603.7i2605.0 
4' -2607. 4 '2309.3 
6;-2611.l|'2613.0 


6 
7 
8 
9 

710 
1 

2 

3 


2103.7 
2107.4 
2111.1 
2114.8 
2118.5 
2122  2 
4  2125.9 
2129.6' 
133.3 
2137.0 
21407 
144  4 
2148.1 


210.5.6 
2109.3 
2113.0 
21167 
2120.4 
21-24.1 
2127. H 
2131.5 
2135.2 
2138.9 
2142.6 
2146.3 
2150.0 


2450.0 
2453,7 


1  '2448  1 

2  2451,9 

3  2455.6  2457.4 
4 '2459.3  2461.1 
6  2463.0''2464.8 
6  2466.7^2468 


'2472  2 
2475.9 
2479.6 


7, '2470.4 

8  2474.1 

9  2477.8 
670  2181.5!'24s3.3 

1 '2485.2 '2487.11 

2  -24.S3.9  -2490.7 

3  2492.6  -2494.4 

4  2  496.3  2498.1 
6  2500.0  2501.8 


G  2503.7 

7  2507.4 

8  2511.1 


1505.6 
:509.3 
2.513.0 


2151.9  2153 
2155.0  2157.4 


21.59.3 
2163.0 
2166  7 
2170.4 
2174.1 
8  2177.8 
2181.5 
2185.2 
2188.9 
2192.6 
2196.3  2198 
-2200.0  2201  8 
2203.7  2205.6 
2207.4'2209.3 
2211  1  2213.0 
•2214.8  2216.7 
9-2218.6  2220.4 
2222.2  2224.1 


2161.1 
216 1..-^ 
2168.5 
217-2.2 
2175  9 
2179  0 
2183.3 
2187.0 
2190.7 
2194.4 


9  2514.8  2516.7 
68  0  2518.5  2520.4 
1-2.522. 2 '2-524.1 
2  2-525.9'25:i7.8 
3 '2-529  ;  '-2-531.-'i 
4:253  {.3  253-5.2 
6  2537.0: -25,-i8.9 


-2-540  7  i  2-542  0 
•2.544.4  2546.3 
'2.548  l''2550.0 
2-551.9 '2553.7 


C90  2555.6  '2-557.4 


1 
2 
S 
4 
6 
C 
7 
8 
9 

700 


'25-59.3  2531.1 
'2563.0  2564.8 
-2-566,7,2-568.5 
2-570.4  2572.2 
'2-574.1 '2575.9 
-2577.8''2579.0 

2581.5  2583.3 
2585.2  2587.0 
2588.9  '2590.7 

1592.6  2594.4 


•2614.8  '2616 
'2618.5''26'20,4 
2322  2  2024,1 
•.!625  1)  '26'27.« 
'2629  6I2H31.5 
'26.33  3:'2635  2 
2637.0  '2638.9 


'2642.6 
2646.3 
2650.O 


'2640.7 
4  2644.4 

6  '2648.1 
6 '2651  9  26.53 

7  2655.6|'26.57.4 

8  26.59.3 '2661.1 

9  2663.0  2664.8 


2638.5 
'2rt72.2 
267-'..9 


720  '2336.7 

1  '2670.4 

2  2374.1 

3  2677.8  2679.6 
4'2681.5  '2633.3 
6l'2685.2  2687,0 
6  2688.9  2690.7 
7|269'2.6  2694.4 
8  '2690,3  2698.1 


9,2700.0 
73O|'2703.7 
1  2707.4 
2:'2711.1 


3  2714.8  2716.7 


4 
6 
6 
7 
8 
9 

740 
1 

o 


2718.5 
2722  2 
272-5.9 
2729.6 


2701.8 
2705.0 
2709.3 
2713,0 


20.4 
2724.1 
'2727.8 
'2731.5 


800 
1 
2 

3 
4 
6 
6 
7 
8 
9 

810 
1 

2 

3 
4 

i 
6 
7 
8 
9 

820 
1 
2 
3 
4 
6 
G 
7 
8 
9 

830 
1 
2 
3 


2733.3  2735.2 
'2737.0  2738.9 


740, 
1744.4 
:743.1 
'2751.9 


2742.0 
2740.3 
27-50.0 
•2753.7 


4  2755!6''2757.4 


9 

750 
1 

2 
3 
4 


-2759.3  2761.1 
-2763.0|2764.8 
-2766.712768.5 
-2770.4'2772.2 
•2774.112775.9 
'2777.8 '2779.6 
-2781.5  2783.3 
'278-5.2  2787.0 
2788.9''2790.7 
792.6  2794.4 
•2796.3  2798.1 

2800.0  2-sOl. 8 
•2803.7  2805.0 
2807.4  2809.3 

2811.1  '2813.0 
761»  2814.8  2816.7 

'2818.5  2820  4 
'2822  2  2824.1 
2825.9  28'27.8 
2829  6  '2831.5 
2833.3  2835. 
■2837.0  2838  9 
'2840  7  2842.6 
•2844  4 '2846.3 
9''2848.1  2.3-50.0 
7  70' 235 1.9  28-53.7 
1' 23-55.6 '28-57.4 

2  2S-59  3'2861 

3  2863.0 '2864.8 

4  2866.T  '2868 

6  2870.4  2872  2 
6 '2874.1  -2875.9 

7  2877.8  •2879.( 

8  '2881.5 '28.83 

9  288-5.2 '2887.0 
780 '288.8.9 '2890,7 

1  2392.6  '2894.4 

2  2896.3  2898. 

3  '2900.0  2901.8 

4  29113.7  2905.(i 
6  2907.4  2909  3 

6  2911.1  2913  0 

7  2914.8  2916 

8  2918.6  2920.4 

9  2922.2  2924. 1 
790  29'25.9  2927.8 

1  '29-29.6  2931.5 

2  '2933.3  '2935.2 

3  2937.0  '2938  9 

4  2940.7  2942.0 
6  2944.4  2946.3 

6  2943.1  2950.0 

7  2951.9  295,3.7 

8  29-55.6  2957.4 

9  29-59.3  2961.1 
800  2963.0  2964.8 


Contents, 
Cu.  Yds. 


B. 


2903.0  -2964.8 
2060.7  2968  5 
2970.4  2972,2 
-2974.1  2975.9 
■2977.8  2979.6 
•2981  5  2983.3 

2985.2  29.S7.0 
■2988.9  2990.7 

2992.6  2994.4 
•29^6.3  2998.1 

3000.0  3001,8 

3003.7  3005.6 

3007.4  3009.3 

3011.1  3i'13  0 

3014.8  3016.7 

3018.5  3020.4 
30^22.2  30-24.1 

3025.9  3027.8 
30-29.6  3031.5 

3033.3  3035.2 

3037.0  3038.9 

3040.7  3042.6 
3044  4  3046.3 

3048.1  30-50.0 
3051.9  3053 
30-55.0  30-57.4 

3059.3  3061.1 
,3063.0  3064.8 
3066  7  3068.5 

3070.4  307-2.2 

3074.1  3075.9 

3077.8  3079.6 

3081.5  3083.3 

3085.2  3087.0 


900 
1 


840 
1 
2 


30  38.9  3090.' 
3092.6  3091.4 
3096.3  3098.1 
3100.0  3101.8 

8  3103.7  3105.0 

9  3107.4 


3111.1 
3114.8 

3118.5 


850 
1 
2 
3 
4 
6 
6 
7 
8 


3  3122.2 


31-25.9 
3129.6 


3109,3 
;113.0 
;ll6.7 
3120.4 
3124.1 
3127.8 

3131.; 


6  3133  3  3135.2 
3137.0 

8  3140.7 

9  3144.4 
3148.1 


3151.9  3153. 
3155.6  31.57.4 
'3159.3  3161.1 
.'3163.0  3164.8 


3166.7 


86 


3170.4  3172 


3174.1 


3177.8  3179.6 
9  3181.5  3183  3 


133,9 
3142.6 
3146.3 
31.50.0 


3168..' 


3175.0 


3187.0 


3185.', 
3188  9  3190 
319'2.6'3194.4 
3  3196.3'3'98.1 
4.3-200.0  3-201.8 
6  3-203.7 1 3-20-5.6 

6  3207.4  3209.3 

7  3211.1  3213.0 

8  3214.8|3216  7 

9  3218  5,32-20.1 
8 70  32-22.2  .3224. 1 

1  3-225,9,3-227.8 

2  32.9  6  3231.5 


3  3-233.3 

4  3237.0 
6  3240  7 

6  3244.4 

7  3-248.1 

8  3'25l.9  

9  3255.6  32-57.4 
88  0  32-59.3  3'261.1 

1  3-263.0 

2  3266.7 

3  3270.4 
413274.1 


3235.-. 
3238  9 
324-2.6 
3246.3 
3^250.0 
3253 


3-264.8 
3-268.5 
3-27-2.2 
3-275.9 


6  3'277.8  3279.6 

6  3'28l.5  3'283.3 

7  3285.2 


8 
9 

890 
1 
2 


3292.6 
3296.3 


3303.7 

3  3307.4 

4  3311.1 
6  3314.8 


3322. 
33z5.9 


33-29.6  3331.5 
900  3333.3  3335.2 


3287.0 
3288.9  3290.7 


3294  4 
3298.1 


3300.0  3301.8 


3305.6 
3309.3 
,3313.0 
3816.7 


331.8.6  3320.4 


3324.1 
3327.8 


Contents, 
Cu.  Yds. 


3333.3  3.335,2 
3337.0  3338.9 
3340.7  3342.6 

3344.4  3346.3 
3.348.1  3350.0 
3351.9  3353.7 
3355.6  3357.4 
3359.3  3361.1 

8:3363.0  3364.8 
9  3366.7  3368.5 


910 
1 
o 


4 
6 
6 
7 
8 
9 

920 


3370  4  3372.2 
3374.1 13375.9 
3377.8  3379.6 
3  3381.5  3383.3 


338.5.2  33>7.0 
3388.9  3390.7 

3392.6  3394  4 

3396.3  3398.1 
34()0.0  3401.8 

3403.7  3405,6 

3407.4  3409.3 

1  3411.1  3413,0 

2  3414.8  3416.7 

3  3418  6  3420.4 

4  34'22.2  34-24.1 

5  34-2.5.9  3427.8 
G  34-29.6  3431.5 

7  3433  3  3436.2 

8  3437.0  3438.9 

9  3440.7  3442.6 
930  3444.4  3446.3 

1  3448.1  3450.0 

2  3451.9  3453.7 

3  3465.6  3457.4 

4  3459.3  3461.1 

5  3463.0'3464.8 

6  3466.7  3468.5 
7^3470.4  3472.2 

8  3474.1  3475.9 

9  3477.8  3479.6 
94  0  3481.5  3483.3 

1 '3435.2  3187.0 
2'3488.9:3490.7 
33492.6,34944 
4|3496.3  3498.1 
5j3-500.0'3501.8 

6  3503.7 13.505.6 

7  , .3507.4  3509.3 

8  3511.1  3613.0 

9  3514  8,3516.7 
950  3518,5  3520.4 

1I3522.2'3524.1 
3525.9'.3527.8 

3  3.529.6'3.531-5 

4  3533.3  3535.2 
6  3-537.0  3-538.9 
6'3540.7  3-54-2.6 
7|3544,4  3546.3 

8  3548.1  3650.0 

9  3551.9  3:^.53.7 
900  35.55.6  3.^.57.4 

1  3.5.59.3  3561  1 

2  3563.0  3564  8 

3  3566.7  3668.5 

4  3570.4  3672  2 
6  3574.1  3575  9 

6  3577.8  3579.6 

7  3-581.5  3.583.3 

8  3585.2  3587.0 

9  3-588.9  3.590,7 
970  359-2.6  3594,4 

1  ;5596.3  3598.1 

2  3600.0  3601.8 
8  3603.7  3605.6 
4  3607.4  3609.3 
6  3611.1  3613.0 

6  3614.8  3616.7 

7  3618.5  3620.4 

8  3622.2  3624.1 

9  3625.9  36-27.8 
980.36-29.6  3631.5 

1  3633.3  3635  2 

2  3637.0  3638.9 

3  3640.7  3612  6 

4  3644.4  3646  3 
6  3648.1  3650.0 

6  3061.9,3663.7 

7  3665.6  3667.4 

8  36-59.3 '366 1.1 

9  3603,0  -MCA  S 
990  .3666.7  3668.5 

1  3670.4  367-2.2 

2  3674.1  3675.9 

3  .3677.8  3679.6 

4  3681.5  3683  3 

5  .3685.2  3687.0 

6  36.88.9  3690,7 

7  3692.6  3694.4 

8  3696.3  3698.1 

9  3700,0  3701.8 
100  0  3703.71 


1 


RATIOS  OF  CORRECTION  FOR  AVERAGE  END  AREA  CALCULATIONS. 


WiniH  OF 
Kt*A)>  ItEU. 


2-12 


16 


18 


20 


22 


24 


20 


28 


30 


Area  of 
11  Kn'l 


1.-25    2  2.5 


2.25   to  100 


100 


100 


H  i^Ut  »r 
Siii^il  Kiiil. 


;  Ifa  io  or 
Arciis. 


1:1 

1:1.2 

1:1,4 

1:1.0 

1:I.S 

1:2 

1:2.5 

1  ::{..> 

1:1 

1:4.5 

J:'. 

!:"».■> 

1:0 

1:0.5 

1:7 

1:7.5 

l:s 

1:S.5 

1:1> 

1:0.5 

1:10 


>f(tlOII 

Viirj  in:; 
I'll  a  I 
SI  OS. 


.001 
.002 
.007 
.012 
.019 
.o:w 
.045 
.056 
.0117 
.070 
.0,S5 

.O'j:? 
.100 

.107 
.11.3 
.119 
.124 
.128 
.133 
.13S 
.112 


1      1  1 


1—5 


Slope. 


Slope. 


6.04  5.2  4.74 


"1.74  4.81  4.41 


Slope. 


Slope. 


1-1 
4.1 

,001 
003 
001 
,010 
014 
,023 
,032 
041 
050 
057 
,065 
071 
077 
0«3 
089 
094 
100 
106 
111 
117 
123 


1:1 


U:l 


}:1 


001  .001 
,004  .004 
.007  .OOS 
012  .01- 
,018  .0-.'2 
,032  .033 
.043  .044 
,0-)5  ,056 
.066  .067 
075  .076 
.083  .084 
,0911.092 
,098  .100 
105  .106 
110.111 
1151,116 
l'-'0.122 
125i.l27 
130  .132 
134  .136 
138. 140 


001 
002 
.004 
.006 
.009 
.016 
.023 
.030 
.1  '38 
.043 
.049 
.055 
,060 
065 
,070 
,075 
079 
,084 
08  S 
092 
097, 


1:1 


.001 
.004 
.006 
010 
.014 
;026 
037 
.047 
.057 
,066 
,074 
,081 
088 
094 
100 
105 
110 
115 
120 
125 
130 


.001 

.004 
.007 
.011 
.015 
.027 
.040 
051 
.061 
070 
,078 

,084 
093 
099 
105 
110 
115 
120 
125 
130 
135 


.001 
.002 
.003 
.005 
.000 
012 
.019 
.026 
.033 
.039 
.044 
.050 
.055 
.060 
.065 
.069 
073 
.077 
082 
086 
.090' 


1:1 


n-.i 


,001  .001 
,003  .003 


,006 
010 


.006 
.010 


014  .014 
,024.026 
,035  .037 


045 
054 


.047 
.056 


062  .065 
,070' 07 
,077|.O80 
084:. 088 
090:  095 
095. 101 
1001.105 
106.111 
1111.116 
116'. 121 
12Lj.l25 
126. 130 


J:l 


.001 
.002 
.003 
.005 
.010 
.016 
.022 
.029 
.035 
.040 
.046: 
.051 
.056 
060 
064 
.068 
.072 
.070 
086 
.084 


m 


001 
.003 
006 
010 
.014 
025 
.035 
.04 
.054 


1:1 

.001 

.003 
.006 
.010 
.014 
,024 
,033 
,042 
,051 
,059  .062 
,066  .070 
,073  .078 
,079  .085 
,085  .091 
0911.097 
09'i'.102 
,101  .107 
106  .112 
1111.117 
116  .121 
120.126 


100 


100 


100 


100 


100 


100 


100 


5.14  4.45  4.1.' 


4.72  4.14  3.884.33  3.87  3.644.00  3,62  3,4 


Slope. 


Slope. 


Slope. 


.71  3.43  3,24:3.47  3.20  3.07  3.24  3.20  2.91 


Slope. 


Slope. 


J:l 


.001 
.002 
,003 
,005 
010 
014 
020 
025 
031 
030 


.001 1.001 
.003  ,003 
.000  .006 
.009  .009 
,013.013 
.022  .024 
.031. 034 
.039  .044 
.048 '.052 


i-.l 


055 
003 


042  .070 


047 
051 
055 
058 
.062 
.005 
.009 
072 


.076 
.082 
.088 
.093 
.098 
.102 
.106 
111 


.0751.110 


.000 
.008 
.075 
.082 
.088 
.093 
.098 
.103 
.108 
.113 
.117 
.122 


.001 
.002 
003 
.005 
,(»10 
.014 
.019 


l:l'li-l 


i:l 


1:1 


li:l 


.001  .001 
,003  .003 
.005  .005 
.008  .009 
.012  .013 
.020  .023 
.028  .033 
037  .042 
.023  .045  .050 
.028  .0.53  .058 
,033  060.060 


.037 
.041 
.045 


.006  073 
.072  .079 
.078  .085 
.049!. 083  .090 
.053'.088  .095 
.0561.093  .100 
.0601,097  .104 
.063'. 102  .109 
,0061,100  .113 
.009!  Ill  .118 


 Lool! 

,0011.003: 

,002'.005 
003  .007 
005 '.Oil 
0091.019 
014!  026 
.034 
.042 
,049 
.056 
.062 
.00  s 
.074 
079 
.084 
.089 
.094 
.098 
.103 
.107 


,019 
022 
026 
030^ 
034 
037 
041 
044 
047 
050 
054 
057 
060 
063 


001 
003 
.005 
.008 
.013 
.021 
.030 
0!9 
.047 
.055 
-062 
009 
.075 
.081 
.086 
.091 
.095 
.100 
.105 
.110 
.114 


1:1 


1:1 


001 
002 

.ro3 

005 
.010 
.013 
017 
021 
024 
.028 
.031 
.034 
037 
040 
043 
047 
050 
,053 
,056 
059 


.001 
.003 
.005 
.007 
.010 
.017 
.025 


1^1 
.001 

.003 

,005 
00,- 
012 
.020 
028 


hi 


.032.036 
.039  .045 


.046 
.053 
.059 
,064 
,070 
,075 
,080 
,084 
088 
,093 
,098 
,102 


.052 
.059 
.066 
.07-/ 
.077 
.082 
.0S7 
.092 
.097 
.101 
.10' 

.110 


001 
,002 
003 
00.51 
,008 
012 
010 
019 
022 
025 
028 
031 
034 
037 
040 
043 
040 
048 
051 
I '54 


1:1 


001 
002 
004 
006 
009 
016 
.023 
03(1 
037 
044 
.050 
055 
060 
065 
.070 
075 
080 
084 
.088 
093 
097 


U:l 


,001 

,003 
,005 
,008 
Oil 
019 
,027 
034 
042 
050 
057 
063 
069 
075 
080 
085 
089 
094 
098 
10-J 
107 


Slope. 


Slope. 


i-.r  1:1  1^:1 


.001  .001 
.002  ,002 
.004  .00 
.000.00 
.009  .010 
.015  .018 
.022  .025 
.029  .033 
.03)  .040 
.041  .048 
.018  .054 
.053  .000 


001 

001 
002 
003 
,000 
010 
013 
010 
019 
022 
025 
027 
030 
033 
036 
03  S 
041 
044 
040 
049 


001 
.001 
,002 
,003 
,005 
008 
Oil 
014 
016 
.019 
021 


I 

1:1  1]:1 


.058 
.063 
06 


00(5 
072 
.077 


.072'.082 
.076  .086 
.080.091 
.084  .095 
.088  ,100 
.092  .104 


.001  .001 
.002  .00--' 
.004  .005 
.006  .00' 
.008  .010 
.014.017 
.021  .024 
027  .<  32 
.034  ,039 
.040  (I4() 
045  .052 
050  .058 
024  .055  .064 
.1126  ,060  .009 
,029  .004  ,074 
031  .008  ,079 
.034  .072  .084 
030  .076  .088 
.039  ,079  .092 
041  .083  .096 
044  .087  .100 


liatioof 
A  reas. 


1:1 

4:1.2 

1:1.4 

1:1.0 

1:1.8 

1:2  I 

l::{  f 

1:8.5 

1:4  I 

1:4.5 

1:.,  I 

i:"i.5 

1:0 

1:0.5 

1:7 

1:7.5 

1:8 

l:-i.5 

1:!) 

l:!».o 


On  Estimating  Earthwork. 

The  accompanying  table  is  designed  to 
facilitate  the  computation  of  earthwork 
after  the  areas  of  the  cross  sections  have 
been  obtained.  The  areas  may  be  ob- 
tained bv  calculation  from  the  field  notes  ; 
or  the  cross  sections  may  be  plotted  and 
tlie  areas  ol)taiiif'd  by  the  plani meter. 
The  foruier  method  is  short  and  easy  in 
a  level  country,  but  where  the  surface  of 
the  ground  is  liroken  and  irregular  the 
latter  method  is  to  be  preferred.  Plotting 
the  cross  sections  also  makes  a  complete 
record  of  the  work,  wdlh  its  classification 
at  every  point,  and  allows  revision  and 
deviation  within  the  limits  to  which  the 
section  is  taken,  by  simply  indicating  the 
position  of  the  centre  line.  Usua'iy  it 
will  be  found  easiest  to  plot  the  rods 
from  a  line  assumed  as  the  height  of  in- 
strument; but  when  the  work  is  extend- 
ed so  as  to  involve  several  heights  of 
instrument  in  the  same  section,  or  when 
the  work  is  to  be  used  for  a  great  i.umber 
of  calculations  for  successive  estimates, 
it  w'll  be  found  cheajjest  to  woik  from 
elevations. 

A  c  'nvtnient  form  for  the  estimate 
sheets  is  here  shown.  In  the  two  first 
columns  arc^  entered  the  stations  and 
plu&>es  at  which  the  cross  sections  are 
taken.  The  column  headed  "  Length  hi 
Feel"  is  filled  up  by  s-ubtracting  the 
nu(ubers  in  these  two  first  columns.  The 
Columns  heade<l  "  Area  of  Cross  Section" 
are  filltd  up  with  areas  obtained  either 
from  calculation  or  from  njfasurement 
by  the  iilanimeter.  In  the  columns  head- 
ed "AviriKje  Area"  avQ  euti^ved  one-half 
the  sums  of  thu  areas  of  adjacent  cross 
sections.  If  preferred  the  sums,  in,-tead 
of  the  half  sufiis,  may  be  used,  in  which 
case  the  final  conttnts  will  be  doubled. 

Tlie  main  columns  of  "  Contents  ia 
Cubic  Y(irds  "  are  now  filled  up  by  aid 
of  accompanying  "  Table  of  Cubic  Yards 
in  Lengths  of  100  Feet"  If  the  lengths 
are  1('0  feet  the  corre>iponding  quantities 
are  simply  transferred  from  the  table.  If 
the  distance  is  50  feet,  one  half  the  quan- 
tity is  transferred.  If  the  distance  is  25 
feet,  one-fourth,  &c.  Usually  the  opera- 
ti(  n  can  be  performed  mentally.  The 
tal)le  being  set  u[)  before  one,  the  arrange- 
ment of  it  is  such  that  the  eye  knows  just 
wiiere  to  strike  for  a  quantity.  There 
are  no  leaves  to  turn.  Quantities  can  be 
entered  as  fast  as  one  can  write.  Blue 
ink  may  be  used  in  writing  quantities  in 
excavati'^u,  and  red  ink  in  writing  quan- 
tities in  e[nbankmeut. 

The  calculation  of  earthwork  by  the 
method  of  averaging  end  areas  is  not 
theoretically  correct,  excepting  ia  the 
two  special  cases :   one  when  the  end 


areas  are  equal,  and  the  other  when  the 
prismoid  has  two  of  its  longitudinal 
bounding  planes  parallel.  As  that  por- 
tion of  every  roadway  prismoid,  which 
lies  between  the  vertical  planes  passing 
through  the  edges  of  the  roadbed  is 
practically  included  in  the  latter  condi- 
tion, it  follows  that  the  variation  from 
the  true  contents,  obtained  from  averag- 
ing end  areas,  lies  outside  the  central 
roadbed  prism,  and  we  may  consider  it  as 
dependent  on  the  four  following  factors : 

1st.  The  ratio  of  the  end  areas  of  the 
prismoid. 

2nd.    The  width  of  the  roadbed. 
3rd.    The  degree  of  the  slope. 
4th.    The  heighth  of  the  section. 

This  variation  has  been  investigated 
with  the  result  shown  in  the  table  called 
"Ratios  of  Correction  for  Average  Fad 
Area  Calculations."  The  manner  of  pro- 
ceeding was  briefly  thus :  With  the  data 
shown  in  the  heads  of  the  columns  in 
the  table,  and  in  the  left  hand  column, 
the  true  contents  of  the  prisms  by  the 
prismoidal  formula  were  found,  as  well 
as  the  contents,  by  averaging  end  areas. 
The  ratio  of  variation  in  many  par- 
ticular cases  being  thus  found,  the  curve 
of  variation  for  each  class  was  formed 
by  measuri.ig  the  ratios  of  end  areas 
on  the  axis  of  abscissas,  and  the  per- 
centages of  variation  on  the  axis  of  ordiu- 
ates.  Some  maxima  and  minima  of  these 
curves  were  also  traced,  which  seemed 
to  differ,  in  extreme  cases,  10  per  cent,  or 
so  from  the  mean  given  in  the  table.  It 
is  believed  these  deviations  will  usually 
counterbalance  one  another.  If  the  work 
is  of  a  peculiar  nature,  so  the  general 
cases  here  worked  out  will  not  api)ly,  cor- 
rections applying  to  it  can  be  worked  out 
and  entered  in  one  of  the  blank  columns. 

To  apply  the  table  of  corrections,  we 
divide  one  area  of  cross  section  by  its 
neighbor,  and  take  from  the  table  its  cor- 
responding ratio  or  percentage  of  correc- 
tion and  nmltiply  the  contents  by  it, 
writing  the  result  in  the  column  headed 
"  Correction."  The  special  case,  when 
one  end  is  zero,  or  ends  at  grade,  is  not 
provided  for  in  table  of  corrections.  For 
this  case  the  correction  is,  the  slope  area 
multiplied  by  one  sixth  the  length.  For 
the  road  bed  area  being  the  base  of  a 
wedge,  the  solidity  is  one-half  base  multi- 
plied by  altitude;  but  the  slope  areas  being 
bases  of  pyramids,  the  solidity  is  one-third 
base  multiplied  by  altitude.  One  half 
which  is  used,  less  one-third,  which 
should  be  use(j,  equals  the  correction,  one- 
sixth.  This  correction,  as  well  as  all 
others,  is  to  be  deducted  from  contents  in 
main  column. 


Estimited  Quantities  in  Grading. 


STA- 
TIONS, 


No. 


AKEA  OF  (  KOSS 

>K(;  ION 
IN  S({U  U£K  •■T. 


KxciiTiition. 


■r  j^'  bitiik- 
~  r  meiit 


117  .50  rnt'coiTences 

II8....I  18, 

 .501.58!  53105 

119, 

 .50  638203 

 854171297 


120 


121 


122 
123 


.030163.325 
526 
,  _  .  595 
..'110243485 


2(.)  cm 
40  cm 

00  31 
80,103 


ends 


cm  com  men  ces08 


.3,34  280.500 


3570(127 
.50  743157 
50870  1,56 

..'821 
30534 

Oil  i:m 
70, 

84 

to  int commences 


314 
209 
187  2-55 
73147 

ends 


AVERAGE  AREA. 


ExcaTation. 


394 
-..034 
....527  A 
-1263'. 
55' 


15j 
72 

218^ 

517 

521.', 
806,1 
845J 
677^ 
267 


341 
108 
212 
280 
270 
12K 


170 
278i 
217 
1.56  J 


171^232 


130 
36^ 


15 
67.^ 
215i 
426 
500^ 
540 
242^ 


280 
5.572 
434i 
201.1 


201 
73,! 


Eni- 

b:ink 
mtnt 


Corrected  Totals, 


CONTtNTS  IN  CUBIC  YARDS. 


ExcaTation. 


16.7 
102.910 
729.632 
1174.1 
083.8 
136  3 
40. 


11.4 

53.3 
101.9 


670.213 

400  8 
2987.0 
1565,7 

752,8 

306.518 


9853.7  98 


9755.71.... 


14  S 
63.9 
200.0 
394  4 
302.9 
150  0 
90.0 


1037 
301.0 
120  6 
679  0 
317.0 
144.4 
41.9 


2945.423 
2922.4!..., 


27.8 
125.0 
399.1 
788.9 
62(3.5 
300.0 
179.0 


207.4 
722,7 
241.3 
908.5 
429,6 
223.3 
84.4 


Em- 
l»aiik, 
mciil. 


25. 1 
25,1 


7.0 
23.8 
.5.1 


.53211  40j_8(); 
627S.I  ....j  82.: 


REMARKS. 


The  error  from  calculation  by  averag- 
ing end  areas  is  not  so  great  as  appears 
at  first  sight,  or  as  it  is  often  represented. 
Taking  isolated  cases,  where  the  ratio  of 
end  areas  is  great,  it  may  be  made  to 
appear  that  the  error  is  10  or  15  per  cent.; 
but  taking  extended  work  the  whole 
error  is  trifling,  the  great  bulk  of  con- 
secutive cross  sections  being  nearly  equal 
to  each  other,  and  the  errors  are  distri- 
buted. The  writer  tested  one  section  of 
28,00  >  cu.  yds.  and  found  the  error  less 
than  one  tiiird  of  one  per  cent.  What 
appeared  to  be  a  section  which  would 
show  great  error  on  account  of  crossing 
several  short  ravines  and  gullies,  con- 
taining some  85,000  cu.  ydn.,  was  less  than 
one-half  of  one  per  cent,  out  of  the  way. 

In  earthwork  there  are  only  two  sides 
of  the  prismoid  perfect  planes,  and  these 
two  are  the  theoretical  planes  of  the 
cross  section.  The  surface  of  the  ground 
is  never  a  perfect  plane.  The  rod,  in 
taking  points  usually  sinks  a  little  in  the 
ground,  the  slopes  are  not  trimmed  exact- 
ly, nor  the  grade  made  perf  ct.  If  there 
is  any  difference  between  the  true  so'i.lity 
and  that  obtained  by  the  method  here 
pKesented,  it  is  the  conviction  wf  the 
writer  that  it  would  he  easier  and  cheap- 
er' for  the  engineer  to  shuvel  it  than  to 
calculate  it. 

The  method  of  calculation  for  earth- 
work should  be  direct  and  simple,  so  it 
can  be  used  «afely  by  assistants  not  speci- 


ally skilled  in  intricate  calculations  It 
is  better  for  the  enQ:ineer  to  spend  much 
of  his  time  in  the  field,  minutely  observ- 
ing and  closely  measuring  the  work,  than 
to  spend  it  mainly  in  the  office,  basing 
refined  computations  on  erroneous  or 
careless  nie;isnrements.  The  errors  in 
measurement  will  usually  be  greater  than 
the  errors  of  calculation,  by  averaging 
end  areas  without  cori-ection. 


—Published  bv — 

JOHN  WILEY  "&  SONS, 
$^cieiitifioJPiil>lisliers 


15  Astor  Place. 


NEW  YORK  CITY. 


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1 


TABLE  OF  CUBIC  YARDS  IN  LENGTHS  OF  100  FEET. 

ADAPTED  ESPECIALLY  TO  THE  CALCULATION  OF  EARTH  WORK  BY  THE  METHOD  OF  ATERAGING  END  AREAS. 


Contents  of  Column  "A"  are  for  the  integers  in  column  headed  "Area,  Square  Feet." 
Contents  of  Column  "  B  "  are  for  the  same  integers  plus  0.5  square  foot. 


Contents  for  lengths  greater  or  less  than  100  are  obtained  by  simple  proportion,  thus:  125 
sq.  ft.  for  length  of  20  ft.=x%=i  of  463.0  cu.  yd.-.;  the  contents  for  125  sq.  ft.=92.6  cu.  yds. 

COPYRIGHT  1885  BY  S.  B.  FISHER. 


Area, 
Sq.  n,. 

Contfpts, 
Cii.  Yds. 

Contents, 
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1835.2 

h 

2203,7  2205.6 

6 

3-)5.6 

357,4 

6 

725.9 

727.8 

611096.3 

1098.1 

G 

1466.7  1468.5 

6,1837.0 

1838.9 

6 

2207,4  2209.3 

7 

3)9.3 

361.1 

7 

729  6 

731.5 

711100.0 

1101.8 

7 

1470.4  1472.2 

7  1840.7 

1842,6 

7 

2211  1  2213.0 

8 

363.0 

364.8 

8 

733  3 

735.2 

8  1103.7 

1105.6 

8 

1474,1  1475.9 

8  1844.4 

1846.3 

8 

2214.8  22:6.7 

9 

loci 

366.7 

368.5 

9 

737.0 

738.9 

9  1107.4 

1109.3 

9 

1477.8 

1479.6 

9  1848.1 

1850.0 

9 

2218.5  2220.4 

370.4 

372.2 

200 

740,7 

742.6 

3eo|iiii.i 

1113.0 

400 

1481.5  1483.3 

500,1851.9 

1853,7 

6OOI2222.2.2224.I 

Contents,  _^  ^ 
Cu.  Yds.  3.1; 

 1 

B.  \^f. 


2242.6 
2246.3 
2250,0 
2253  7 
22-57.4 
2261,1 
2264.S 
2268.5 
2272.2 
2275.9 
2279.6 
2283  3 
2287,0 


600  2222.2  2224  1 

1  [2225.9  2227.8 

2  2229,6  2-231.-5 
3'2233  3  22.35.2 
4'2237,0  223S,9 
5'2240.7 
62244.4 
712248.1 

8  2251.9 

9  2255.6 
610  22-59,3 

1  2263  0 

2  2266.7 

3  2270.4 

4  2274.1 

5  2277.8 
G  2281.5 
712^85  2 

8  2238  9 '2290. 

9  2292.6  2294,4 
620  2296,3  2298.1 

1  2300.0  2301.8 

2  2303.7  2305,6 

3  2307.4  2309.:'. 

4  2311.1  2313.0 

6  2314  8  2316,7 

6  2318  5  2320.4 

7  2322.2 '2324.1 

8  2325  9  2327.8 

9  23-29.6 '2331..'; 
03  0  23;}3.3  2.335.2 

1  2337.0  233 -i.O 

2  2340.7 1 2342  6 

3  2344  4  2346.3 

4  2348.1  23.50.0 

5  2351.9  23-53 
6-2355  6  2357.4 

7  2359,3  2361.1 

8  2363.0  2364.8 

9  2366.7  2368.5 
640  2370,4  2372.2 

1  2374.1  2.375.9 

2  2377.8  2379.6 

3  2331.5  2383  3 
"4  2:?35.2  2387.0 

6  2388.9  2390.7 

6  2392.6  2394  4 

7  2396.3  23911 

8  2400.0  2401.8 

9  2403.7  2405.6 
650  2407.4  2409.3 

1  2411.1  2413,0 

2  2414.8  2416  7 

3  2418,5  24-20.4 

4  2422  2  2424  1 

5  2425.9,2427  8 

6  2429.6  2431.5 

7  2433  3  2435,2 

8  2437.0  2438  9 
9, 2440.7 1 24  42.6 

660  -2444  4  2446.3 


Conients, 
Co.  Yds. 


B. 


2450.0 
2453,7 


1  2448  1 

2  2151,9 

3  2455.6  2457,4 

4  2459,3  2461.1 
5'2463.0  2464.8 


G'2466.7 


2468  5 


7  2470.4  24721 

8  2474.1  2475.9 
9!2477.8  2  479.6 

6  7  0  2  481.5j24S3.3 

1  2485.2  2487,0 

2  2433.9  2490.7 

3  2492.6'2494.4 

4  2496.3  2498.1 

5  2-500.0  2-501.8 
G  2503.712605.6 

7  2507.4  2509.3 

8  2511.l|25l3.0 

9  2514.8  2516,7 
680,2518.5  2520.4 

1  2-522.2  2524.1 

2  2525.9  2527.8 

3  2^29  ;  2531.-5 

4  253  {  3  2-53.5.2 
6 '2537.0  25.-t8.!) 

6  2-540  7  2-542  6 


2544.4  2546.:! 
2.348  1' 2-550.0 
9  2-551.9  2-5.53.7 
69  0  25.55.6  2-5.57.4 


9 

700 


25-59.3  2561.1 
2563.0  2564.8 
2566,712568.5 

2570.4  2-572.2 
2-574.1 '2576.9 
2577.8  2579.6 

2581.5  2583.3 
8  2585,2  2587.0 

588.9  2590.7 

2592.6  2594.4 


7  ->0  -2592.6  2.594.4 

1  12-596.3  2-598.1 

2  2600,0  2601.8 

3  2603.7i2605,6 

4  2607.4  2609.3 

6  -2611.112613.0 
G  -2614.8  2616.7 

7  2618.5  2620,4 

8  2622,2  2624,1 

9  2625,9!2627.--< 
710  2629  6f2ri31.5 

1  26.33  3^2635  2 

2  2637.0  2638.9 

3  2640.7  2642,6 

4  2614.4  2646.3 
6 1 26  48.1  26.50.0 

6  2651  9  26.53.7 

7  2655.6|2657.4 

8  26-59.3  2661.1 
9l2'i63.0  2664,8 


720,2366.7 
1  2670.'',, 
2|2374.1 

3  2677.8 

4  2631.5 
51268-5.2  268/, 

6  2688.9  2690 

7  2692.6  2694.4 
8i2696,3  2698.1 


2668 

2ii72.2 

267-5,9 

2679.() 

2653,3 


9  2700.0 
73O'2703.7 


1  2707.4  2709,3 
2713,0 


2701.8 
2705.6 


9 

r4f) 
1 


2!2711,1 
3  2714.8  2716 
2718.5j2720.4 
2722  2  2724.1 
272-5.9  2727,8 
2729.6  2731.5 
2733.3 
2737.0 
2740.7 
2744.4 
2743.1 
3  2751.9 


5 
6 
7 
8 
9 

750 
1 
2 

3 
4 


8 
9 

76<» 
1 

2 
3 
4 
5 
G 
7 


2735.2 
2733.9 
,2742,6 
2746,3 
2750.0 
2753.7 
4'27.55.6'2757.4 


2759.3  2761.1 
2763.0;2764.8 
-2766.712763.5 
2770.4'2772.2 
2774.l|2775.9 
•2777.8  2779.0 
2781.5  2783.3 

2785.2  2787.0 
2788.9  2790.7 

7920  2794.4 

2796.3  2798.1 

2300.0  2^>01.8 

2803.7  2805.6 
-2807.4  2809,3 

2811.1  2813.0 

2814.8  2816.7 
2318.5  2820  4 
•2322,2  2324,1 
28-25,9  2827.8 
•28*29  6  2.331.5 
2333.3  2835.2 
2837,0  2838  9 
2840  7  2842,6 

8  •2844,4  2846.3 

9  2848.1  28.50.0 
770'2851.9  28.53.7 

1 '23-55.6  28-57.4 

2  •2359  3  2861.1 

3  2863.0  2864.8 

4  2866.7  2868.5 
6  2870.4  2872  2 

6  2874,1  2875.9 

7  2877.8  2879.0 

8  2881.5  28H3.:! 

9  2385,2  2887.0 
780  2.SS8.9  2890  7 

1  2392.6  2894.4 

2  2896.3  2898.1 

3  2900.0  2901.8 

4  29' 13.7  290.5.6 
6  2907.4  2909  :! 

6  2911.1  2913  0 

7  2914.8  2916,7 

8  2918.5  2920.4 

9  2922,2  2924,1 
790  2925.9  2927.8 

1  2929,6  2931.5 

2  29;i3.3  2935.2 

3  2937.0  2938  9 

4  2940.7  2942,6 

6  2944.4  2946,3 
G  2943.1  2950.0 

7  2951.9  2953.7 

8  2955.6  2967,4 

9  2959.3  2901.1 
800  2963,0  2964.8 


800 
1 
2 

3 
4 
5 
6 
7 
8 
9 

810 
1 

2 
3 
4 
I 
C 
7 
8 
9 

82(1 
1 
2 
3 
4 
5 
G 
7 
8 
9 

830 
1 
2 
3 
4 
5 
G 
7 
8 
9 

84o 
1 
2 


850 
1 

2 
3 


Contents, 
Cu.  Yds. 


A. 


2963.0  -2964.8 
2966.7  2968  5 
2970.4  2972,2 
■2974.1  2975  9 
•2977.8  2979,6 
•2981  5  2983,3 
2985.2  2987.0 
•2988.9  2990.7 

2992.6  2994.4 
29^6.3  -2998,1 
.3000.0  3001  8 

3003.7  3005.6 
3007,4  3009.3 
.■Ml  1.1  3013  0 

3014.8  3016.7 
,3018.5  3020.4 

3022.2  3024.1 

3025.9  .3027.8 
3029,6  3031.5 

3033.3  303-5.2 
;5037.0  3038.9 
;3040.7  3042.6 
3044  4  3046.3 
:3018.1  30-50,0 
3051.9  3053.7 
3055.6  3057.4 
,30.39.3  3061.1 
3063.0  3064.8 
3066  7  3068.5 

3070.4  30722 
.3074,1  3075.9 

3077.8  3079,6 

3081.5  3083.3 
.3035.2  3037.0 

3038.9  3090.7 

3092.6  3094.4 
3096.3  3098.1 
3100.0  3101.8 

3103.7  3105.0 


3107.4 
3111.1 
3114.S 
3118..3 
3  31222 
3125.9 
3129.0 


3133  3  3135  2 


3137.0 

8  3140.7 

9  3144.4 
3148.1 
3151.9 
3155.6 

3159.33161.1 
4  3163,0  3164.8 


86 

1 

2 


3166.7 


3170.4  3172 


3174.1 
3'.77.8 
9  3181,5 


3109  3 
3113.0 
3116,7 
3120.4 
3124.1 
3127.8 
3131.5 


3133,9 
3142.0 
3146.3 
3150.0 
31.53.7 
3157.4 


3168.5 


3175.0 
3179,6 
3183  3 
3185.2  3187.0 
3188  9  3190, 
31926  3194.4 

3  3196.3  3198 

4  3-200.0  3-201.,S 
6  3203.7|3205.6 

6  3207.4  3209.3 

7  3211.1  3213.0 

8  3214.8|3216  7 

9  ;?218  5  3220.4 
870  32-22.2  3^224. 1 

1  3-2-25.9  3-227.8 

2  32.9.6  3231.5 

3  3233.3  3235.2 

4  3237.0:3238  9 

6  3240  7j32426 
G  3244.4  3246,3 

7  3248,1|3250.0 

8  3251,9  3253,7 
3257.4 


9  3255.6 


880  32.59,3  3261.1 


890 
1 
2 


1  3263,0 

2  3266, 

3  3-270.4 
4'3274,1 
6:3277,8 
6'.328l,5 
7  3-285,2 
8 
9 

3296.3 


,3303. 
3!3307.4 
4  3311.1 


3314.8 
;5318.5 
332-2.2 
33-/5.9 
3329.6 


900  3333.3  3335.2 


3-264.8 
3268.5 
3272.2 
3275.9 
3279.(i 
3283..i 
3287.0 
3-288.9  3290,7 
3292.6  3294  4 
3298.1 
3300.0  330 l.K 


3305.6 
;«09.3 
.3313.0 
3316.7 
3320.4 
5324.1 
3327.8 
3331.5 


900 
1 
2 
3 
4 
5 


7 
8 
9 

910 
1 

2 

3 
4 
5 
6 
7 
8 


Contents, 
Cu.  Yds. 


A.  B. 


3333.3  3335  2 
3337.0  3338.9 
3340.7  3342.6 

3344.4  3346.3 
3:548.1  33.50,0 
3351.9  33.53.7 

6  3355.6  33.57.4 
:5359.3  3361.1 
3363.0  3364,8 
9  3366.7  3368,5 
3370  4  337-2.2 
.3374.1  3,375.9 
3377.83379.6 
:5381.5  3:133,3 
338-5.2  33>7,0 
3388.9  3390.7 
3392.6  3394  4 
3396.3  3398.1 
3400.0  3401.8 
9  3403  7  3405  6 
920.3407.4  3409.3 
l!3411.1  34130 
2;;5414.8  3410.7 

3  3418  6  3420,4 

4  34-22  2  3424.1 
6  342.5.9  3427,8 

6  3429.6  3431,5 

7  3433  3  3435.2 

8  3437.0  3438.9 

9  3440.7  3442.6 
9  3  0  3  444.4  3446.3 

1  3448.1  34,50.0 

2  3451.9  3453.7 

3  3455.6  34.57.4 
434.59.3  3461. 1 

5  3463.0'3404.8 
G  3466.7 13463.5 
7,3470.4,3472,2, 
8|3474,1  3475,9 
9  3477,8  3479,6 

940  3431.5'3483.3 
1 '3435.23 187.0 

2  3488.9|3490.7 

3  3492.6  3494  4 

4  3496.3  3498.1 
5,3500.0'3.501.8 
G  3.503.7  3,505.6 
7 :.3507.4  .3509.3 

8  3511.l'3513.0 
9,3514.8'3516.7 

950  3518.53520.4 
1|3522.2  3524.1 
:  352,5.9'3527.8 

3  3529.6'3.531.5 

4  3-533.3  353,3.2 

5  3-337.0  3-5,38.9 
6;3540.7  3-542.6 
7:3544,4  3546.3 
8[3-548.1  35,50.0 

9  3551.9  3553,7 
960  3.5-55.6  3.'^57.4 

1  3.559.3  3561  1 

2  3.563.0  3.564  8 

3  3566.7  3.')68,6 

4  3570.4  3.572  2 

6  3574.1  3575  9 

6  3577.8  3,579.6 

7  3581.5  3.583.3 

8  3585.2  3587.0 

9  3-588.9  3590,7 
970  3.592,6  3.594.4 

1  3596.3  3598.1 

2  3600.0  3i;ol,8 
8  3603.7  3()05.6 
4  3607.4  3609.3 
6  3611.1  3613.0 

6  3614.8  3616.7 

7  3618.5  36-20,4 

8  36222  3624.1 

9  36-2.5.9  ,36-27,8 
980  3629.6  3631.5 

1  36;}3.3  3635  2 

2  3037.0  3638.9 

3  3640.7  ,3642  6 

4  3644.4  ,3(i4(>  3 

6  3648.1  3650.0 
G  3651.9,3653.7 

7  ,3655.6  3657.4 
8.36,59.3.3661.1 
9  3663.0  :5664,8 


990  3666.7 


3(;68.5 


1  3670.4  3672,2 

2  :5674.I  3675.9 

3  3677,8  3079.6 

4  3681.6  3683  3 

5  368.5.2I3687.O 
G  3688.9  36!)0,7 

7  .3692.6  3694.4 

8  3696.3  3698.1 

9  3700.0  3701.8 
100  0  3703.71 


RATIOS  OF  CORRECTION  FOR  AVERACE  END  AREA  CALCULATIONS. 


WIDTH  OP 
UUAI)  BED. 


Area  of 
11  I'n.l 


l.'J5    2  2.5 


H  ih-lit  lit' 
Kiii  iil  Kiiil, 


lla  io  of 
Knil 
Areas. 


1:1 

1:1.2 

1:1.4 

]:!.(> 

1:1. S 

1:2 

1:2..> 

]::S 

1  ::$..> 

1:1 

1:4.5 

!:"> 

^:^.^> 

1:(; 

1:«..> 

1:7 

1:7.5 

1:S 

l:s.5 

!:!> 

1:<.>.5 

1:10 


^»■l•tiOIl 
Varj  iiif; 
Ml  a  1 
Si  I's. 


.001 
.002 
.007 
.012 
.019 
.0,S3 
.015 
.056 
.0(i7 
.07(3 
.OSo 
.093 
.100 
.107 
.113 
.119 
.124 
.128 
.133 
.13S 
.142 


Slope. 


i:l 


001 

003 
005 

mo 

()14 

,023 
,032 
041 
,050 
057 
,065 
071 
,077 
083 
0«i» 
094 
100 
106 
111 
117 
123 


1:1  1.5:1 

001  .001 
.004  .004 
.007  .008 
,012  .012 
,018  .02 
,032  .033 
.043  .044 
,0  "i5  ,056 
,066  .067 
,075  .076 
,083  .084 
,09lj.092 
,093'. 100 
,105  .100 
110  .111 
115|.116 
120.122 
1251.127 
130  .132 
134.136 
138.140: 


2  12 


2.25   to  100 


14 


100 


1—5 


Slope. 


6.04  5.2  4.74 


Slope. 


1-1 


.001 
.002 
.004 
.006 
.009 
.016 
.023 
.030 
.038 
.043 
,049 
.055 
,060 
065 
,070 
,075 
079, 
,084 
088 
092 
097 


1:1  1^:1 


.001 
.004 
.006 
010 
.014 
;02fi 
037 
.047 
,057 
,066 
,074 
,081 
088 
094 
100 
105 
110 
115 
120 
125, 
130 


.001 
.004 
.007 
.011 
,015 
.027 
,040 
.051 
,061 
,070 
,078 
,084 
093 
,099 
105 
110 
115 
120 
125 
130 
135 


}:1 


.001 
.002 
.003 
.005 
.006 
012 
.019 
.026 
.033 
.039 
.044 
.050 
.055 
.060 
.065 
.069' 
.073 
.077 
082 
086 
.090. 


1:1  1J:1 


16 


18 


100 


5,74  4.81  4.41 


Slope. 


i:l 


,001  .001 
.003  .003 


.006 
.010 
.014 
.026 
.037 
.047 
.056 
.065 


.006 
.010 
.014 
.024 
.035 
.045 
.054 
062 

.070|.07 
.077|.030 
.084'.088 
,09o' 095 
,095  .101 
,100  .105 
,106.111 
1111.116 
,116'. 121 
12l|.125 
126  .130 


.001 
.002 
.003 
.005 
.010 
.016 
.022 
.029 
.035 
.040 
.046 
.051 
.056 
060 
064 
068 
.072 
.076 
086 
.084 


1:1 


.001 

.003 
.006 
.010 
.014 
.024 
.033 
.042 
.051 


U:l 


001 
.003 
006 
010 
014 
025 
.035 
047 
.054 


,059  .062 
,066  .070 
,073  .078 
,079  .085 
,085.091 
,0911.097: 
09')'. 102 
,101  .107 
106  .112 
1111.117 
116  .121 
120'. 126 


100 


5.14  4.45  4.13  1.72  4.14  3.88  4.33  3.87  3.644.00  3.62  3.43 


Slope. 


J:l 


.001 
.002 

,003 
,005 
010 
014 
020 
025 
031 
036 
042 
047 
051 
055 
058 
.062: 
.065 
069 
072 
075 


^Ijl^l 

.001  [.001 
.003,-003 
.006  .006 
.009 '.009 
.013.013 
.022  .024 
.0311.034 
.039  .044 
.0481.052 


20 


100 


Slope. 


i:l 


055 
063 
.070 
.076 
.082 
.088 
.093 
.098 
.102 
.106 
111 
.116 


.060 
.068 
.075 
.082 
.088 
.093 
.098 
.103 
.108 
.113 
.117 
.122 


001 
.002 
003 
.005 
010 
014 
019, 


1:1  li:l 


.001  .001 
.003  .003 
.005  .005 
.008  .009 
.012.013 
.020  .023 
.028  .033 
037  .042 
,023'.045  .050 
028  .053  .058 
033  060.066 


.037 
.041 
.045 
.049 
.053 
056 
,060 


.066  .073 
.072  .079 
.078  .085 
.083  .090 
.088  .095 
.093  .100 
,097  .104 
063' 102.109 
,066  .106  .113 
069'. 111'. 118 


100 


24 


100 


Slope. 


Slope. 


1:1  1^:1 


 LOOl 

,001 1.003 
,002.005 
003  .007 
,005 '.Oil 
009  .019 
014'. 026 


,019 
,022 
026 
030 
034 
037 
041 
044 
047 
050 
054 
057 
060 
063 


.034 
.042 
.049 
.050 
.002 
.06,-s 
.074 
079 
.084 
.089 
.094 
.098 
.103 
.107 


.001 
.003 
.005 
.008 
.013 
.021 
.030 
0!9 
.047 
.055 
OO-J 
060 
.075 
.081 
.086 
.091 
.095 
.100 
.105 
.110 
.114 


1-1 


1:1 


001 
002 

ro3 

005 
.010 
.013 
.017 
021 
.024 
028 
031 
.034 
.037 
040 
043 
.047. 
050 
053 
.056 
059 


.001 
.003 
.005 
.007 
.010 
.017 
.025 
.032 
.039 
.046 
.053 
.059 
.064 
.070 
.075 
.080 
.084 
088 
.093 
.098 
.102 


.001 
.003 
.005 
.00.- 
.012 
.020 
028 
036 
.045 
.052 
.059 
.066 
.07 -J 
.077 
.082 
.0S7 
.092 
.097 

.101 

.10'- 

.110 


26 


28 


100 


100 


30 


100 


3.71  3.43  3.24|3.47  3.20  3.07  3.24  3.20  2.91 


Slope. 


i:l 


001 
.002 
,003 
005 
,008 
,012 
016 
019 
022 
025 
028 
031 
034 
037 
040 
043 
046 
048 
051 
054 


1:1  U:! 


001 
002 
004 
006 
009 
016 
.023 
030 
.037 
044 
.050 
055 
.060 
.065 
.070 
,075 
,080 
084 
.088 
093 
097 


.001 
.003 
.005 
.008 
.011 
019 
.027 
.034 
042 
.050 
057 
063: 
069 
075 
.080 
.085 
089 
094 
.098 
10-J 
107 


Slope. 


I  I 


.001  .001 
.002  .002 
.00  i  .005 
.006.007 
.009  .010 
.015  .018 
.022  .025 
.029  .033 
.035  .040 
.041  .0+8 
.018  .054 
.053  .060 


001 
001 
002 
003 
,006 
010 
013 
016 
019 
022 
025 
027 
030 
033 
036 
03-i 
041 
044 
046 
049 


.058 
.063 
067 
.072 


.066 
072 
.077 
.082 


.076  .086 
.080.091 
.084  .095 
.088  ,100 
.092  .104 


Slope. 


001 
,001 
,002 
.003 
005 
008 
Oil 
014 
.016 
019 
021 


l:l'lj:l 


.001  .001 
.002  .002 
.004  .005 
006.00' 
.008  .010 
.014'.017 
.021 '.024 
.027  .032 
034  .039 
.040  .<I46 
045  .052 
.050  .058 
024  .055  .064 
026  .060  .069 
029  .064  .074 
031  .068  079 
034  .072  .084 
.036  .076  .088 
039  .079  .092 
041 .083  .096 
044  087  .100 


Itatio  of 
Eiiil 
A  rras. 


1:1 

1:1,2 

1:1.4 

1:1.6 

1:1.8 

1:2 

1:2.5 

1:3 

1:3.5 

1:4 

1:4.5 

1:.> 

1:5.5 

1:6 

1:6.5 

1:7 

1:7.5 

1:8 

1:1.5 

1:1) 

I:!).  5 


On  Estimating  Earthwork. 

The  acc(jmpanying  table  is  designed  to 
facilitate  the  cotnputatiou  of  earthwork 
after  the  areas  of  the  cross  sections  have 
been  obtained.  The  areas  may  be  ob- 
tained by  calculation  from  the  field  notes  ; 
or  the  cross  sections  may  be  plotted  and 
the  areas  obtained  by  the  plani meter. 
Tlie  former  method  is  short  and  easy  in 
a  level  country,  but  where  the  surface  of 
the  ground  is  broken  and  irregular  the 
latter  method  is  to  be  preferred.  Plotting 
the  cross  sections  also  makes  a  complete 
record  of  the  work,  with  its  classification 
at  every  point,  and  aUows  revision  and 
deviation  within  the  limits  to  which  the 
section  is  taken,  by  sim[)iy  indicating  the 
position  of  the  centre  line.  Usua'iy  it 
will  be  found  easiest  to  plot  the  rods 
I'rom  a  line  assumed  as  the  height  of  in- 
strument ;  but  when  the  work  is  extend- 
ed so  as  to  involve  several  heights  of 
instrument  in  tlie  same  section,  or  when 
the  work  is  to  be  used  for  a  great  i. ember 
of  calculations  for  successive  estimates, 
it  will  be  found  cheapest  to  work  from 
elevations. 

A  cmvinient  form  for  the  estimate 
sheets  is  here  shown.  In  the  two  first 
columns  are  entered  the  stations  and 
pluf-~es  at  which  the  cross  sections  are 
tiiken.  The  Column  headed  "Length  in 
Feet"  is  filled  up  by  subtracting  the 
numbers  in  these  two  first  columns.  The 
Columns  headed  "  Area  of  Gross  Section  " 
are  filhd  up  with  areas  obtained  either 
from  calculation  or  from  measurement 
by  the  planimett^r.  In  the  columns  head- 
ed "Average  Area"  are  entered  one-half 
the  sums  of  the  areas  of  adjacent  cross 
sections.  If  prei'erred  the  sums,  in>tead 
of  the  half  sums,  may  be  useil,  in  which 
case  the  final  conttnts  will  be  doubled. 

The  main  columns  of  "  Contents  in 
Cubic  Yards  "  are  now  filled  up  by  aid 
of  accompanying  "  Table  of  Cubic  Yards 
in  Lengths  of  100  Feet"  'if  the  lengths 
are  liiQ  feet  the  corresponding  quantities 
are  simply  transferred  from  the  table.  If 
the  distance  is  50  feet,  one  half  the  quan- 
tity is  transferre<l.  If  the  distance  is  25 
feet,  one-lburth,  &c.  Usually  the  opera- 
tion can  be  performed  mentally.  The 
table  being  set  up  before  one,  the  arrange- 
ment of  it  is  such  that  the  eye  knows  just 
where  to  strike  for  a  quantity.  There 
are  no  leaves  to  turn.  Quantities  can  be 
entered  as  fast  as  one  can  write.  Blue 
ink  may  be  used  in  writing  quantities  in 
excavation,  and  red  ink  in  writing  quan- 
tities in  embankment. 

The  calculation  of  earthwork  by  the 
method  of  averaging  end  areas  is  not 
theoretically  correct,  excepting  ia  the 
two  special  cases :   one  when  the  end 


areas  are  equal,  and  the  other  when  the 
prismold  has  two  of  its  longitudinal 
bounding  planes  yiarallel.  As  that  por- 
tion of  every  roadway  prismoid,  which 
lies  between  the  vertical  planes  passing 
through  the  edges  of  the  roadbed  is 
practically  included  in  the  latter  condi- 
tion, it  follows  that  the  variation  from 
the  true  contents,  obtained  from  averag- 
ing end  areas,  lies  outiide  the  central 
roadbed  prism,  and  we  may  consider  it  as 
dependent  on  the  four  following  factors  : 

1st.  The  ratio  of  the  end  areas  of  the 
prismoid. 

2nd.    The  width  of  the  roadbed. 
3rd.    The  degree  of  the  slope. 
4th.    The  heighth  of  the  section. 

This  variation  has  been  investigated 
with  the  result  shown  in  the  table  called 
"Ratios  of  Correction  for  Average  End 
Area  Calculations."  The  manner  of  pro- 
ceeding was  briefly  thus:  With  the  data 
shown  in  the  heads  of  the  columns  iu 
the  table,  and  in  the  left  hand  column, 
the  true  contents  of  the  prisms  by  the 
prismoidal  formula  were  found,  as  well 
as  the  contents,  by  averaging  end  areas. 
The  ratio  of  variation  in  many  par- 
ticular cases  being  thus  found,  the  curve 
of  variation  for  each  class  was  formed 
by  measuri.ig  the  ratios  of  end  areas 
on  the  axis  of  abscissas,  and  the  per- 
centages of  variation  on  the  axis  of  ordin- 
ates.  Some  maxima  and  minima  of  these 
curves  were  also  traced,  which  seemed 
to  differ,  in  extreme  cases,  10  per  cent,  or 
so  from  the  mean  given  in  the  table.  It 
is  believed  these  deviations  will  usually 
counterbalance  one  another.  If  the  work 
is  of  a  peculiar  nature,  so  the  general 
cases  here  worked  out  will  not  apply,  cor- 
rections applying  to  it  can  be  worked  out 
and  entered  in  one  of  the  blank  columns. 

To  apply  the  table  of  corrections,  we 
divide  one  area  of  cross  section  by  its 
neighbor,  and  take  from  the  table  its  cor- 
responding ratio  or  percentage  of  correc- 
tion and  multiply  the  contents  by  it, 
writing  the  result  in  the  column  headed 
"  Correction."  The  special  case,  when 
one  end  is  zero,  or  ends  at  grade,  is  not 
provided  for  in  table  of  corrections.  For 
this  case  the  correction  is,  the  slope  area 
multiplied  by  one  sixth  the  length.  For 
the  road  bed  area  being  the  base  of  a 
wedge,  the  solidity  is  one-half  base  multi- 
plied by  altitude ;  but  the  slope  areas  being 
bases  of  pyramids,  the  solidity  is  one-third 
base  multiplied  by  altitude.  One  half 
which  is  used,  less  one-third,  which 
should  be  used,  equals  the  correction,  one- 
sixth.  This  correction,  as  well  as  all 
others,  is  to  be  deducted  from  contents  in 
main  column. 


Estimated  Quantities  in  Grading. 


STA 
TIOSS. 


AVERAGE  AREA. 


Cnt  comneGces 


30 


11750 

118...."  18,  16 

 50158|  53105 

119 

 506382635 

85417|297 


120 


121 


123 


.630:163325 
26 

_  .  595 

..'110243485 


cmcoiiiiDen  ces68 

31 


12250870156209 


ends 


20 
40 
60 

80103 
.....3.34280.560 

35700  277  555 
50  743157 


1S7 


3147 


,'821 
.30534 

Hii  m 

70 
84 

0  mt  coimences 


ends 


314 
209 
255 


9 


 394 

 634 

 527. 

263: 
55 


15| 
72 
218^ 
517 
521  i 
806J 
845.5 
677^ 
267 


341 
108 
212 
280 
270 


121^  242^ 


170 
278.; 
217 
156J 
17U 
130 
36 1 


15 
67  J 
215^ 
426 
560^ 
540 


280 

557^ 
434.! 
26U 
232 
201 
73^ 


Em- 

liHnk- 
nient 


Corrected  Totals, 


COSTtNI.S  IN  CUBIC  YARDS. 


Excavation. 


16.7  1 
162.916 
729.632 
1174.1 
683.8 
136  3 
40.7 


11.4 
53.3 
161.9 
670.2 
400  8 
2987.0 
1565 
752.8 
306.518 


9853.7  98 


14  8 

63.9 
200.6 
394  4 
302.9 
150  0 

90.0 


103  7 
361.0 
120  6 
579  6 
317.6 
144.4 
41.9 


2945.423 


9755.7|....  2922.4....  5278. 


:::  u 

c  = 


27.8 
125.0 
399 
788.9 
626.5 
300.0 
179.6 


207.4 
722.7 
241.3 
968.5 
429  6 
223.3 
84.4 


Em- 
liank- 
iiK'nl. 


25.1 
25.1 


7.6 
23.8 
5.1 


46j_8(V/ 
..i  82.7  ....j 


UEllARKS. 


The  error  from  calculation  by  averag- 
ing end  areas  is  not  so  great  as  appears 
at  first  sight,  or  as  it  is  often  represented. 
Taking  isolated  cases,  where  the  ratio  of 
end  areas  is  great,  it  may  be  made  to 
appear  that  the  error  is  10  or  15  per  cent.; 
but  taking  extended  work  the  whole 
error  is  trifling,  the  great  bulk  of  cm- 
secutive  cross  sections  being  nearly  equal 
to  each  other,  and  the  errors  are  distri- 
buted. The  writer  tested  one  section  of 
28,(j0  >  cu.  yds.  and  f)und  the  error  less 
than  one-third  of  one  per  cent.  What 
appeared  to  be  a  sectitm  which  would 
show  great  error  On  account  of  crossing 
several  short  ravines  and  gullies,  con- 
taining some  85.000  cu.  yds.,  was  less  than 
one-half  of  one  per  cent,  out  of  the  way. 

In  earthwork  there  are  only  two  sides 
of  the  prismoid  perfect  planes,  and  these 
two  are  the  theoretical  planes  of  the 
cross  section.  The  surface  of  the  ground 
is  never  a  perfect  plane.  The  rod,  in 
taking  points  usually  sinks  a  little  in  the 
ground,  the  slopes  are  not  trimmed  exact- 
ly, nor  the  grade  made  perfi  ct.  If  there 
is  any  difierence  between  the  true  so'i  iity 
and  that  obtained  by  the  method  here 
presented,  it  is  the  conviction  of  the 
writer  that  it  would  be  easier  and  cheap- 
er for  the  engineer  to  shovel  it  thau  to 
calculate  it. 

The  method  of  calculation  for  earth- 
work should  be  direct  and  simple,  so  it 
can  be  used  safely  by  assistants  not  speci- 


ally skilled  in  intricate  calculations.  It 
is  better  for  the  engineer  to  spend  much 
of  his  time  in  the  field,  minutely  observ- 
ing and  closely  measuring  the  work,  than 
to  spend  it  inainly  in  the  office,  basing 
refiued  computaiions  on  erroneous  or 
careless  measurements.  The  errors  in 
measurement  will  usually  be  greater  than 
the  errors  of  calculation,  by  averaging 
end  areas  without  cori-ection. 


— Piiljlislied  by — 

JOHN  WILEY  &  SONS, 
Scientific.*  I*  ixtolisliers 


1,5  Astor  Place. 


NEW  YORK  CITY. 


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